Pipelines undergo sequential stages before failure caused by high-pH stress corrosion cracking. These sequential stages are the incubation stage, intergranular crack initiation (Stage 1a), crack evolution to provide the condition for mechanically driven crack growth (Stage 1b), sustainable mechanically driven crack propagation (Stage 2), and rapid crack propagation to failure (Stage 3). The crack propagation mechanisms in Stage 1b are composed of the nucleation and growth of secondary cracks on the free surface and crack coalescence of secondary cracks with one another and the primary crack. These mechanisms continue until the stress intensity factor (K) at the crack tip reaches a critical value, known as KISCC. This investigation took a novel approach to study Stage 1b in using precracked compact tension (CT) specimens. Using precracked specimens and maintaining K at less than KISCC provided an opportunity to study crack initiation on the surface of the specimen under plane stress conditions in the presence of a pre-existing crack. In the present work, the effects of cyclic loading characteristics on crack growth behavior during Stage 1b were studied. It was observed that the pre-existing cracks during Stage 1b led to the initiation of secondary cracks. The initiation of the secondary cracks at the crack tip depended on loading characteristics, i.e., the amplitude and frequency of load fluctuations. The secondary cracks at the crack tip can be classified into four categories based on their positions with respect to the primary crack. Low R-ratio cycles generated an evident cyclic plastic zone, where high density of intergranular cracks were formed. The higher the frequency of the low R-ratio cycles, the higher the density of the intergranular cracks forming in the cyclic plastic zone. The crack growth rate increased with an increase in either the amplitude or the frequency of the load fluctuations. The minimum and maximum crack growth rates were 8 × 10−9 mm/s and 4.2 × 10−7 mm/s, respectively, with the R-ratio varying between 0.2 and 0.9, frequency varying between 10−4 Hz and 5 × 10−2 Hz, and at a fixed stress intensity factor of 15 MPa√m. It was found that avoiding rapid and large load fluctuations slowed down crack geometry evolution and delayed the onset of Stage 2. The implication of these results for pipeline operators is that reducing internal pressure fluctuations by reducing the frequency and/or amplitude of the fluctuations can expand Stage 1 and increase the reliable lifetime of operating pipelines.

INTRODUCTION

Any failure of a buried oil and gas transmission pipeline may pose a risk to human safety, the environment, the economy, and the assets of the company and the country1-3  because of the highly pressurized and flammable oil and gas inside the pipeline. Hence, the integrity management of the buried pipelines is of paramount importance, and several methods and measurements have been developed to promote the safe operation of the pipelines. For instance, pipes are protected against corrosion with the simultaneous application of cathodic protection and coatings to isolate the pipe from the local corrosive environment.4-8  However, failure in the coating might result in the formation of occluded environments at the coating defect that are breeding grounds for environmentally assisted cracking (EAC).

One of the common EAC mechanisms in pipeline steel is high-pH stress corrosion cracking (HpHSCC).9-10  The first occurrence of HpHSCC dates back to 1965 in Louisiana, United States.11-12  Although many efforts have been made to understand the causes for HpHSCC and the remedies to mitigate it, the average rate of in-service failure caused by HpHSCC is about 1.5 failures per year for U.S. transmission pipelines over the last few decades.13-14  HpHSCC failures keep happening during hydrostatic tests in North American pipelines.15  The average age of pipelines that underwent HpHSCC failures is 20 y to 30 y.16  This indicates the possibility that HpHSCC increases as the age of the pipeline increases. A piece of evidence for this implication is the incidence of HpHSCC in Russia, where it was believed that only near-neutral pH stress corrosion cracking threatens the buried pipeline.17  Therefore, it is of paramount importance to improve the understanding of HpHSCC crack evolution and enhance the current modeling to protect pipelines against HpHSCC threats. The current modeling is based on the bathtub model proposed by Parkins, as discussed briefly in the following paragraph.

Parkins proposed the bathtub model to show the time-dependent HpHSCC crack propagation behavior3,14,18  for this form of EAC. According to the bathtub model, pipelines experience five sequential stages leading to a failure caused by HpHSCC, as shown in Figure 1. The first stage, which is labeled as the “incubation stage” in Figure 1, is the time required to establish the appropriate environmental conditions that cause HpHSCC before cracking begins. Two requirements can characterize the potent environment established after a coating failure: the formation of a high-concentration aqueous carbonate-bicarbonate solution and the partial loss of cathodic protection near the coating defects.3  The second stage, which is denoted as “Stage 1a” in Figure 1, is characterized by the emergence of short and shallow intergranular cracks on the pipe’s surface beneath the coating. These cracks initially propagate at a high rate; however, they become dormant once they reach a limiting size of about 50 μm in depth.19  Work hardening in the neighboring areas20  is one possible reason for the dormancy of the cracks at this stage. As the crack propagates, a passive film forms on the cracks’ walls. The passive film might block the path of the corrosive environment to the crack tip and prevent further dissolution. Additionally, the plane strain condition in the depth tip reduces the amount of plasticity and can be considered an additional possible reason for the dormancy of the cracks in Stage 1a. Using experiments on tapered specimens, Parkins proposed a threshold stress for crack initiation, i.e., the intergranular cracks nucleate at multiple sites if the stress exceeds a threshold value.21-22  After their initiation, the cracks propagate in a stochastic manner so that the cracks, once initiated, experience periods of growth and dormancy.3,23-24  This stage is shown as “Stage 1b” in Figure 1. The crack growth at this stage is either by reactivation of the existing crack or by coalescence of adjacent cracks. The crack evolution at this stage continues until relatively long and deep cracks form on the free surface.25  From the fracture mechanics point of view, the stress intensity factor at the depth tip (Kdepth) of the crack at the end of Stage 1b reaches the threshold stress intensity factor for HpHSCC (KISCC).3,26-27  Thereafter, Stage 2 starts when the mechanical driving force at the crack tip causes sustainable crack growth through the film rupture mechanism.12,28-32  The crack growth rate increases significantly in comparison with the previous stage. Therefore, the intergranular crack advances in the pipe’s thickness within a relatively short time frame compared to Stage 1b. The crack propagation at this stage reduces the residual strength of the pipe significantly. Crack propagation at this stage is followed by Stage 3, where rapid crack growth results in immediate rupture and fracture of the pipe.

FIGURE 1.

Schematic illustration of the bathtub model for HpHSCC.30 

FIGURE 1.

Schematic illustration of the bathtub model for HpHSCC.30 

According to the above description and Figure 1, Stage 1b is the lifetime-determining stage in pipes vulnerable to HpHSCC. A recently published review paper that studies the chronological crack evaluation during HpHSCC failures20  showed that much research is devoted to the incubation stage,33-35  Stage 1a,18,22,24,36  and Stage 2.28-30,32  In contrast, less attention had been paid to Stage 1b of HpHSCC.20  The development of the bathtub model rests on the assumption that crack initiation and crack coalescence are random. Therefore, it is assumed that cracks propagate in a stochastic manner, i.e., independent of existing cracks and loading conditions. It is of interest to identify the preferential regions for crack initiation during Stage 1b if they exist. Preferential crack initiation in the vicinity of the existing crack followed by crack coalescence shortens Stage 1b. Therefore, understanding the HpHSCC crack growth at this stage is essential to predict the remaining lifetime of pipes susceptible to HpHSCC. The novelty of the current study is to study the crack propagation in Stage 1b regarding the loading condition and pre-existing cracks.

This research is designed to investigate the role of loading conditions on crack propagation during Stage 1b. To simulate Stage 1b, a novel approach was used in which the side faces of the CT specimens were analyzed for crack initiation as a function of stress under plane stress conditions. Note that the stress intensity factor was kept less than KISCC. The crack morphologies on the side faces of the precracked CT specimens were studied to identify the preferential crack initiation in the crack tip plastic zones. The crack growth rates under different loading conditions were measured based on the crack length on the fracture surfaces of the CT specimens. The correlation between crack growth behavior and loading conditions is discussed.

EXPERIMENTAL PROCEDURES

Materials and Environment

Steel samples from a microalloyed line pipe steel with a wall thickness of 12 mm and an outer diameter of 1,067 mm were used in this study. The chemical composition of the steel is reported in Table 1. Figure 2 shows the stress-strain curve of the steel used in this study. The ultimate tensile stress for this steel is 637 MPa. This particular steel shows discontinuous yielding, which is also known as the yield point phenomenon. The upper and lower yield points for this steel are 560 MPa and 555 MPa, respectively.

Table 1.

Elemental Composition of the Microalloyed Line Pipe Steel Used in This Study

Elemental Composition of the Microalloyed Line Pipe Steel Used in This Study
Elemental Composition of the Microalloyed Line Pipe Steel Used in This Study
FIGURE 2.

The stress-strain response of the microalloyed line pipe steel used in this study.

FIGURE 2.

The stress-strain response of the microalloyed line pipe steel used in this study.

As noted in the Introduction, Stage 1b represents the condition that a crack is pre-existing, and the stress intensity factor at the pre-existing crack tip is smaller than KISCC. The Stage 1b crack growth mechanism is the initiation of the secondary crack on the free surface, followed by merging the newly initiated cracks to the primary crack. The secondary cracks initiate under the plane stress condition and possess smaller dimensions compared to the primary cracks. Therefore, the stress intensity factor at their cracks’ tips is not as high as that of the primary crack. To simulate this condition, precracked specimens were needed in the current study. Additionally, the maximum applied load at the tip of the pre-existing crack was chosen to be smaller than KISCC. This experiment design allows the study of the new crack initiation under the plane stress condition in the vicinity of the pre-existing crack. Further details about the precracked specimens and the loading conditions can be found in the following paragraph and Loading Parameter section, respectively.

CT specimens with the linear dimensions shown in Figure 3 were machined from the line pipe so that the notches were parallel to the longitudinal direction of the pipe. The specimen configuration allows the cracks to propagate perpendicular to the hoop direction, i.e., in the same direction as the typical cracks in the field.37  Sample preparation involved mechanically polishing by abrasive papers up to 600 grit, followed by ultrasonic cleaning in acetone for 15 min. Fatigue precracking was conducted in air according to the ASTM E647-08 standard to produce a sharp crack tip at the notch of the machined specimens.38  Crack initiation near the notch tip could be in varied orientations, such as the direction with maximum shear stress. The crack propagation path is a zigzag at higher magnification. However, the propagation direction is perpendicular to the maximum tensile load on a global scale. The precrack length on each side of the specimens was measured at certain intervals in compliance with ASTM E647-08. The final length of the precrack on each side of the specimens was controlled to be 2.5 ± 0.2 mm. A schematic illustration of the precracked CT specimen and its dimensions is shown in Figure 3. Using the precracked CT specimens provides the ability to control the stress intensity factor at the crack tip. Hence, the crack can be maintained in Stage 1b because the mechanical loading condition for Stage 2 has not been met. Equation (1) expresses the stress intensity factor at the crack tip.
formula
where P and B are the applied load to precracked CT specimens during the test and specimen thickness, respectively. The parameters a and W are parameters depending on the dimensions of the precracked CT specimens, as shown in Figure 3. For the CT specimens in this study, a and W are 13.6 mm and 40 mm, respectively. In Equation (1), f (a/W) represents a dimensionless factor related to the geometry of the precracked CT specimen, and it is a function of a and W as shown in Equation (2):
formula
FIGURE 3.

Schematic illustration of the precracked CT specimen used in this study.

FIGURE 3.

Schematic illustration of the precracked CT specimen used in this study.

For each test, two separate cells were used so that the two specimens replicated each other. Each cell involved a precracked CT specimen, which acted as a working electrode. The potential of the CT specimens was maintained at −590 mV versus the standard calomel electrode (mVSCE) by using a potentiostat. This potential of the CT specimens was initially selected within the potential range for HpHSCC reported in the literature.13  Additionally, further potentiodynamic polarization tests conducted in this study proved that the steel used here is susceptible to HpHSCC when the potential is between −575 mVSCE and −625 mVSCE, as will be discussed in the Results and Discussion section. The auxiliary electrode for the cell was a stainless steel ribbon that surrounded the CT specimen. An aerated aqueous solution composed of 0.5 M Na2CO3 and 1 M NaHCO3 at a temperature of 40 ± 0.2°C was used as an electrolyte for the cell. The electrolyte was identical to the standard electrolyte for HpHSCC (1 N Na2CO3 and 1 N NaHCO3); however, the temperature was somewhat different (40°C rather than 75°C) to fit the context of the Canadian pipeline industry. The authors’ previous work has demonstrated intergranular cracking under the test conditions using potentiodynamic polarization tests at two scan rates.30  The corrosion fatigue tests started 24 h after setting up the test cell to allow the cell to reach equilibrium in temperature and potential. It is worth mentioning that a black film covered the side faces the CT specimens after 24 h of exposure to the test environment. The loading conditions for the tests will be described later in the Loading Parameters section.

Poteniodynamic Polarization Tests

The fast (33 mV/s) and slow (0.33 mV/s) scan rate potentiodynamic polarization tests were performed in a solution of 0.5 M Na2CO3 and 1 M NaHCO3 at 40°C to evaluate the electrochemical response of the steel under the environmental conditions in this study. Rectangular coupons with linear dimensions of 10 mm × 10 mm × 9 mm were cut from the line pipe steel. The coupons were mounted in epoxy so that a face with the area of 1 cm2 remained uncoated. Preparation of the coupons includes mechanical polishing by abrasive papers up to 600 grit and cleaning in ethanol. A Gamry Reference 600 workstation using a three-electrode cell system was used for electrochemical measurements. The three-electrode cell was composed of a prepared coupon as a working electrode, a platinum plate as a counterelectrode, and a SCE as a reference electrode. The potential range for potentiodynamic polarization tests was between −1,000 mVSCE and 1,000 mVSCE.

Loading Parameters

A horizontal loading machine was used to apply different loading waveforms to the pinhole-loaded precracked CT specimens. The authors’ previous research39  showed that the precracked CT specimen is at Stage 1b of HpHSCC crack growth when Kmax is equal to or below 15 MPa√m. Therefore, a Kmax of 15 MPa√m was selected for all of the loading scenarios in this study. In total, nine constant-amplitude loading waveforms were designed to study the effects of either amplitude or frequency of load fluctuation on Stage 1b of HpHSCC crack growth. The range of R-ratio (min. stress/max. stress) was 0.2 to 0.9, and the frequency range was 10−4 Hz to 5 × 10−2 Hz. Table 2 summarizes the characteristics of the applied constant-amplitude loading waveforms in this study.

Table 2.

Details of Constant-Amplitude Loading Waveforms

Details of Constant-Amplitude Loading Waveforms
Details of Constant-Amplitude Loading Waveforms

Determination of Crack Growth Rate

After each test, a passive black film formed on the side surfaces of the CT specimens in contact with the HpHSCC test solution. It has been shown that this black film is composed of iron carbonate and iron oxide.29,40  The exposed surfaces were polished slightly using an oil-based suspension of alumina to remove the black film. Afterward, the polished surfaces were etched with Nital (5%) to permit the study of the crack path and the grain structure using scanning electron microscopy (SEM). Then, all of the CT specimens were fractured at liquid nitrogen temperatures to expose both fracture surfaces. An aqueous solution composed of 8 N HCl and 3.5 g/L hexamethylenetetramine was used to remove the passive films covering the crack fracture surfaces. The fracture surfaces were studied using SEM, and the lengths of primary and secondary intergranular cracks were measured on the fracture surfaces. The reported crack growth rates reflect the crack length on the edges of fracture surfaces, i.e., crack propagation rates on the side faces of the CT specimens.

RESULTS AND DISCUSSION

Electrochemical Response of the Steel in the Test Solution

Figure 4 illustrates the fast and slow scan rate potentiodynamic polarization curves of the unstressed steel in a solution of 0.5 M N2CO3 and 1 M NaHCO3. The steel showed active-passive behavior under the test condition for both fast and slow scan rate tests. The slow scan rate test is used to detect film formation and here indicates a progressive film formation. According to the slow scan rate potentiodynamic polarization curve, the corrosion potential and the primary passive potential are −855 mVSCE and −650 mVSCE, respectively. Conversely, the fast scan rate will minimize film formation, which represents significant anodic activity because of film rupture events. Comparing fast and slow scan rate tests, there is a particular potential range where the electrochemical response of steel varies from significant anodic dissolution in film-free condition to insignificant activity when the required time for film formation is provided. This potential range is labeled as the HpHSCC potential range in Figure 4, and it is known as the active-to-passive transition region. Two criteria were applied to determine the potential range in Figure 4. First, the fast scan rate current density must exceed 1 mA/cm2. Second, the differences between the fast and slow scan rate must be greater than one order of magnitude.28,30,35,41-42  According to Figure 4, the HpHSCC potential range is between −625 mVSCE and −575 mVSCE.

FIGURE 4.

Fast (33 mV/s) and slow (0.33 mV/s) scan rate potentiodynamic polarization curves of the steel in a solution of 0.5 M Na2CO3 and 1 M NaHCO3 at a temperature of 40°C along with a determination of potential range for HpHSCC by comparing the fast and slow scan rate tests.

FIGURE 4.

Fast (33 mV/s) and slow (0.33 mV/s) scan rate potentiodynamic polarization curves of the steel in a solution of 0.5 M Na2CO3 and 1 M NaHCO3 at a temperature of 40°C along with a determination of potential range for HpHSCC by comparing the fast and slow scan rate tests.

When the steel is exposed to the test solution at the potential of −590 mVSCE, intergranular corrosion occurs on the free surface of the steel, followed by the formation of a passive film on the grains and the penetrating tip of the intergranular corrosion. Therefore, unstressed steel experiences intergranular etching under the test condition. However, the passive film is brittle and prone to rupture upon applying adequate mechanical driving force. If the mechanical driving force ruptures the passive film on the grain boundaries, intergranular corrosion proceeds and forms intergranular cracks.3,20,35,43-44  Therefore, there is a threshold value that provides a film-free condition on the grain boundaries. The physical meaning of the threshold is the mechanical driving force that provides a film-free condition on the grain boundaries. In other words, the mechanical driving force fractures the passive film on the grain boundaries and suppresses repassivation. Consequently, dissolution at the grain boundaries forms intergranular cracks. Similarly, intergranular cracks propagate through dissolution at the grain boundaries unless a passive film forms on the crack tip.

The Magnitude of Load Fluctuations

Constant-amplitude loading schemes with different R-ratio and frequencies were applied to precracked CT specimens, where the Kmax was kept at 15 MPa√m for each waveform. The range of fluctuation in stress intensity factor was from 1.5 MPa√m to 12 MPa√m, associated with R-ratios of 0.9 to 0.2. The maximum and minimum frequencies were 5 × 10−2 Hz and 10−4 Hz, respectively. Accordingly, the duration of one cycle was between 20 s and 10,000 s. All of the test conditions result in crack advance on the sides of the CT specimens, but no crack growth was observed in the middle section through the thickness of the CT specimens. Thus, this condition can be considered as crack propagation in Stage 1b.39 

Figure 5 depicts the area near the precrack tip on the side faces of the CT specimens tested under three different R-ratios after polishing away the passive film and etching in Nital (5%). The frequency load cycles with an R-ratio of 0.9 were 5 × 10−2 Hz, whereas the frequencies for R-ratios of 0.7 and 0.5 were 10−2 Hz. As can be seen, the crack morphology near the precrack tip is different for each R-ratio, although the Kmax for all test conditions was the same. Figure 5(a) shows no significant intergranular crack propagation for the R0.9_F5E-2 test condition. In contrast, R0.5_FE-2 test conditions resulted in a colony of intergranular cracks at the precrack tip, as shown in Figure 5(c). Figure 5(b) illustrates the crack morphology under the R0.7_FE-2 test condition. Propagation of an intergranular crack from the precrack tip is evident, along with evidence of secondary crack initiation in the adjacent areas. These observations imply that the propensity for intergranular cracking near an existing crack increases as the amplitude of load fluctuation increases.

FIGURE 5.

Crack tip morphologies at the area near the precrack tip tested under constant-amplitude loading conditions with different R-ratios: 0.9 at 5 × 10−2 Hz (a), 0.7 at 10−2 Hz (b), and 0.5 at 10−2 Hz (c).

FIGURE 5.

Crack tip morphologies at the area near the precrack tip tested under constant-amplitude loading conditions with different R-ratios: 0.9 at 5 × 10−2 Hz (a), 0.7 at 10−2 Hz (b), and 0.5 at 10−2 Hz (c).

Frequency of Load Fluctuation

Figure 6 displays the area near the precrack tip on the side faces of CT specimens tested under constant-amplitude loading waveforms with an R-ratio of 0.5 at three different frequencies after polishing away the passive film and etching in Nital 5%. In this figure, two distinctive regions can be considered according to fracture mechanics principles, viz. the crack tip plastic zone and the elastic zone. The large dashed red curve shows the theoretical crack tip plastic zone (ry) calculated by Equation (3). In this equation, ry is the radius of the plastic zone under plane stress condition, KI is the mode I of stress intensity factor, σys is yield strength, and θ is the angle between the crack plane and material element.
formula
FIGURE 6.

The intergranular crack morphologies on the free surfaces of the CT specimens tested under constant-amplitude waveforms for R-ratio = 0.5 at frequencies of 10−4 Hz (a), 10−3 Hz (b), and 10−2 Hz (c).

FIGURE 6.

The intergranular crack morphologies on the free surfaces of the CT specimens tested under constant-amplitude waveforms for R-ratio = 0.5 at frequencies of 10−4 Hz (a), 10−3 Hz (b), and 10−2 Hz (c).

Equation (3) is based on the Von Mises criterion, where yielding occurs when the effective stress is equal to yielding. Additionally, the theoretical plastic zone in Equation (3) is based on an elastic crack-tip solution, in which redistribution of stress after yielding is neglected. Further discussion about the theoretical plastic zone is given in the Determination of Crack Growth Rate section (stress condition at the crack tip).

There are a number of intergranular cracks on the side faces of the CT specimens, and the intergranular crack density increases as the frequency increases. The intergranular cracks can be classified into four categories with regard to their relative position from the fatigue-precrack tip, as will be discussed later in the Classification of the Secondary Cracks at the Crack Tip section.

Regardless of the position of the secondary cracks, the reason for crack growth is anodic dissolution along the grain boundaries. In general, when the HpHSCC environment is established, intergranular corrosion occurs on the surfaces exposed to the HpHSCC environment. However, the intergranular corrosion is gradually reduced, as passive films form at the tip of the intergranular corrosion crack. Therefore, unstressed steel exposed to the HpHSCC environment shows intergranular etching. However, the brittle passive film can be ruptured at grain boundaries by an adequate amount of mechanical driving force, and then dissolution proceeds until the passive film reforms. Here, the critical mechanical driving force is the strain rate, i.e., the amount of strain generated over time. This implies that the amount of strain and the time frame in which the strain is generated are equally important. The amount of strain must exceed the fracture ductility of the passive film, and the time for fracturing the passive film must be short enough to prevent repassivation. Otherwise, any fracture of the passive film is healed by repassivation. If the passive film’s rupturing rate surpasses the repassivation rate at some grain boundaries, corrosion at those grain boundaries proceeds, and those boundaries undergo intergranular cracking. The physical meaning of threshold stress is the stress condition that provides a sufficient strain rate to crack the passive film at the grain boundaries. Crack initiation happens at multiple sites,3,20,24  although all of the grain boundaries are prone to cracking theoretically.21  These newly nucleated cracks can merge with each other and form longer cracks.23-24  For the intact steel pipeline, it has been shown that there is a threshold stress that can provide the requirement for crack initiation.21-22  The threshold value for the stress for crack initiation is about at the yield stress, and it decreases under cyclic loading conditions.21-22  Metallurgical discontinuities assist the crack initiation by altering the stress state at the crack tip and locally providing the microscale threshold stress.3,39,45-46  Accordingly, the pre-existing cracks intensify the stress in the adjacent area and increase the chance for crack initiation.39  Stage 1b in HpHSCC crack growth, where an intergranular crack exists on the free surface, represents the situation mentioned above. In the same manner, the fatigue precrack CT specimens used in this study represent the same situation. Hence, the stress condition at the crack tip is of paramount importance.39,46 

Stress Condition at the Crack Tip

From a fracture mechanics point of view, when the cracked structure is loaded uniaxially, the stress state near the precrack tip will be biaxial or triaxial in the cases of plane stress and plane strain conditions, respectively. Additionally, the stress state near the crack tip will be intensified so that the stress at this region is higher than the nominal stress applied to the body. Figure 7 illustrates a cracked body under a Y-direction uniaxial loading condition. The intensified stress condition in the Y-direction (σy) under plane stress condition, existing on the free surface, is shown in Figure 7. The complete elastic solution for σy on the crack plane (θ = 0) is described by Equation (4). In this equation, K is the stress intensity factor, and x is the distance from the crack tip. In this equation C, D, and E are constants.47 
formula
FIGURE 7.

Schematic representation of the cyclic plastic zone, the theoretical plastic zone, and the actual plastic zone at the primary crack loaded under cyclic loading conditions and corresponding stresses from the stress-strain curve.

FIGURE 7.

Schematic representation of the cyclic plastic zone, the theoretical plastic zone, and the actual plastic zone at the primary crack loaded under cyclic loading conditions and corresponding stresses from the stress-strain curve.

According to Equation (4), the stress approaches the nominal stress for large x. In the case of load fluctuation, the K in Equation (4) is used to present the maximum stress intensity factor. All of the terms except the first one become negligible when x approaches zero. The first term increases toward infinity as x decreases. This behavior is shown with the dashed blue line in Figure 7. However, plastic deformation happens in the real material so that stress will not increase much further than yielding, and it depends on the three-dimensional stress state and the appropriate yield surface for that state. Therefore, there is a plastic region at the crack tip, as discussed in the following paragraphs.

According to Equation (4), the stress follows a decreasing trend with increasing x, and it becomes equal to the yield strength of the material at a point that marks the boundary of the plastic zone. For the plane stress condition, like the stress condition on the free surface, yielding occurs when σy equals the yield strength of the material. Assuming that the boundary between elastic and plastic occurs when the stress satisfies the yield criterion, the first-order estimate of the plastic zone can be calculated by Equation (5). It is worth mentioning that this equation is identical to Equation (3) on the crack plane (θ = 0). The first approximation is also known as the theoretical plastic zone, and it is shown with a dark blue circle in Figure 7.
formula
According to Figure 7, σy is greater than yield strength in the theoretical plastic zone. The second-order estimate of the plastic zone size is based on the redistribution of those stresses to satisfy equilibrium. The load capacity in the theoretical plastic zone is limited by yielding. Hence, the stresses higher than the yield point must be bypassed around the plastic zone. Redistribution of the extra stresses causes more material to yield and expands the plastic zone. A simple force balance leads to Equation (6), which provides a second-order estimate of plastic zone size under a plane stress condition.47  The second-order estimate is also known as the actual plastic zone and is shown with a light blue circle in Figure 7. According to Equation (6), the actual plastic zone size is about twice the theoretical one.47  Additionally, note that the plastic zone shape can be determined by Equation (3); however, here, it is assumed θ = 0 for the sake of simplicity.
formula
The above analysis of the theoretical and actual plastic zones’ formation considered monotonic loading conditions. However, it has been additionally proposed that a cyclic plastic zone forms at the crack tip in the presence of cyclic loading.48  The cyclic plastic zone can be defined by damage accumulation models, which were developed to explain fatigue crack growth behavior. According to the damage accumulation model, the crack tip materials are divided into small blocks, as shown in Figure 8. Under cyclic loading conditions, different amounts of damage are accumulated in those material blocks depending on their position relative to the crack tip. There are three different zones at a crack tip subjected to cyclic loading conditions, viz. the cyclic plastic zone, the monotonic plastic zone, and the elastic region. The elastic zone, which is far ahead of the crack tip, is the same as that defined in Figure 7. The materials located in the elastic zone deform in a purely elastic manner. The materials located in the monotonic plastic zone deform plastically during loading to the maximum stress state allowed by the yielding condition. Outside that zone, only elastic deformation takes place during the loading-unloading of each load cycle. The monotonic plastic zone size varies systematically with the maximum stress applied to the crack body or the maximum stress intensity factor, as shown in Equation (6). The third zone, known as the cyclic plastic zone, forms close to the crack tip. The load fluctuations in this region form a complete hysteresis loop. Therefore, materials located in this region undergo plastic deformation in every load cycle.48-50  The cyclic plastic zone shape and size depend on R and the ΔK value. Several empirical equations estimate the cyclic plastic zone size.51  Its radius can be estimated as a quarter of the monotonic plastic zone radius.48  Irwin proposed Equation (7) to estimate the plastic zone size (rCPZ) for plane stress conditions.51 
formula
FIGURE 8.

Schematic illustration of the damage accumulation model for fatigue crack propagation.

FIGURE 8.

Schematic illustration of the damage accumulation model for fatigue crack propagation.

The cyclic plastic zone is the region where cumulative plastic strain is generated. According to damage accumulation, the fatigue crack propagates once the cumulative level of plastic strain fully damages a material block. Given that the intergranular crack propagation happened during the test conditions, the cumulative strain in the cyclic plastic zone provides the mechanical driving force for passive film rupture, as will be discussed in the Classification of the Secondary Cracks at the Crack Tip section.

Classification of the Secondary Cracks at the Crack Tip

Figure 9 shows typical crack morphologies on the side faces of the CT specimens. This specimen is chosen because it has an intermediate density of secondary cracks in the crack tip region. In this figure, the area near the crack tip is divided into 15 squares so that each one has an area of 0.01 mm2. The density of cracks at each square was determined with the use of ImageJ software. As is evident, the maximum crack density is right at the crack tip. The density of the secondary cracks decreases as the distance from the precrack tip increases so that the density becomes less than 1% beyond the theoretical plastic zone. However, the initiation of a relatively long crack was observed at the boundary between the actual theoretical plastic zones. The condition that leads to the formation of these cracks will be discussed in this section with regard to their relative distance from the fatigue precrack tip and the stress condition. The intergranular cracks on the side faces of the precracked CT specimens can be classified into four categories, as labeled in Figure 9 and discussed below.

  • Group I: Crack initiated at the boundary of the theoretical plastic zone.

FIGURE 9.

Analysis of the density of intergranular cracks at the area near the precrack tip. The numbers in each square show the density of the intergranular cracks. Using software, the intergranular crack density is calculated through dividing the total area of the cracks in each square by the area of each square. Example of the crack categories: crack initiated at the boundary of the theoretical plastic zone (I), crack initiated within the theoretical plastic zone (II), cracks initiated in the cyclic plastic zone (III), and crack initiated from the precrack tip (IV).

FIGURE 9.

Analysis of the density of intergranular cracks at the area near the precrack tip. The numbers in each square show the density of the intergranular cracks. Using software, the intergranular crack density is calculated through dividing the total area of the cracks in each square by the area of each square. Example of the crack categories: crack initiated at the boundary of the theoretical plastic zone (I), crack initiated within the theoretical plastic zone (II), cracks initiated in the cyclic plastic zone (III), and crack initiated from the precrack tip (IV).

Figure 10 shows the crack labeled as I in Figure 9 at higher magnification. Here, a total of six small intergranular cracks with individual lengths below 100 μm have been initiated. These small intergranular cracks are labeled as “AB,” “CD,” “EF,” “GH,” “IJ,” and “KL.” As mentioned earlier, the crack propagation in the depth direction is initially rapid.3  However, the crack propagation rate gradually decreases, and newly initiated cracks reach the limiting size of 50 μm.19-20  It has been shown that the cracks at this stage have a semi-elliptical shape, where the crack length on the surface, 2c is larger than the crack depth, a.3,19-20,39  Given that these cracks are in the early stage of growth and given their short length on the surface, it can be estimated that these cracks are shallow. Hence, the stress intensification near these cracks’ tips will be relatively small20  and can be neglected in this study. Reviewing both experimental and field data, Parkins found empirically that neighboring cracks tend to merge and form larger cracks on the surface if the conditions for Equation (8) are met. In this equation, y is the normal distance between two cracks, and 2cm is the average length of two adjacent cracks.20-21,24  The tendency for coalescence is conspicuous in Figure 10 as the nearest tips of two adjacent cracks are bending to link the cracks. Hence, from point A to point L can be considered as a single crack.
formula
FIGURE 10.

Evidence of crack initiation and crack initiation and crack coalescence along the boundary of the theoretical and the actual plastic zones. This figure depicts a higher magnification of the crack labeled I in Figure 9, which is composed of the following six smaller cracks: “AB,” “CD,” “EF,” “GH,” “IJ,” and “KL.”

FIGURE 10.

Evidence of crack initiation and crack initiation and crack coalescence along the boundary of the theoretical and the actual plastic zones. This figure depicts a higher magnification of the crack labeled I in Figure 9, which is composed of the following six smaller cracks: “AB,” “CD,” “EF,” “GH,” “IJ,” and “KL.”

From the previous explanations, the metal in that region transmits the high stresses in the plastic zone to the surrounding metal. Hence, the stress in this region can be about at the yield stress. According to Figure 2, this particular steel has an upper and lower yield point and yield point elongation. The yield point phenomenon represents the condition that the stress decreases when the dislocations start gliding. In the materials showing yield point phenomena, dislocations are locked because of either the high density of dislocations (dislocation locking) or atmosphere pinning by segregated interstitial atoms in the dislocation core.52-53  Hence, the stress increases to the upper yield point to release locked dislocation. After that release, the dislocation motions generate a considerable amount of strain at an extremely high strain rate, which is also known as strain shock.46  The strain rate, generated by strain shock, is sufficient in this region to fracture the passive film on a considerable number of grain boundaries and to sustain intergranular corrosion. Further progress of the intergranular cracking through the grain boundaries at the film-free conditions will form intergranular cracks.

The condition in Figure 10 is an ideal representative for Stages 1a and 1b in a small scale of intact steel pipeline. Accordingly, a few cracks were initiated at multiple sites and merged to form longer cracks. It has been shown that these cracks are not deep, and their crack growth decreases over time so that they reach a maximum limiting depth of 50 μm.19  However, the crack coalescence increases the driving force for crack propagation in the depth direction. Considering the small depth of such cracks, the adjacent stress field is relatively small compared to that of the prefatigue crack tip, and it is ignored here.

  • Group II: Crack initiated within the theoretical plastic zone.

The second group of the intergranular cracks is nucleated in the theoretical plastic zone. According to Figure 9, the intergranular crack density is reduced in the theoretical plastic zone compared to the cyclic plastic zone. The condition that produces this group of cracks is identical to the situation at the narrow sections of the tapered specimens tested under cyclic loading conditions with maximum stress greater than the yield strength. As a side note, a tapered specimen is a tensile specimen in which the cross-sectional area decreases linearly from one end to another end in the gauge section. The tapered specimen’s geometry allows for applying a variety of stresses to a single specimen to determine the threshold stress for crack initiation.21  Obviously, the stress increases from the wide end to the narrow end. Some important points have been established by using tapered specimens. First, the threshold value is about the yield point under a monotonic loading condition.21  Second, cyclic loading reduces the threshold value for crack initiation so that Parkins proposed that every 0.1 decrease in R-ratio reduced the threshold value by about 81 MPa.21  Third, the propensity for crack initiation increases under cyclic loading conditions.22  As for the narrow tip of the tapered specimen, the local stresses exceed the yield point at the theoretical crack tip plastic zone. Additionally, the load fluctuation assists the crack initiation. Therefore, the density of the cracks in this region increases as the magnitude of the load fluctuation increases. Additionally, the orientation of these cracks is not perpendicular to the applied load direction. These cracks are inclined toward the group I cracks (cracks at the boundary of the theoretical plastic zone), and this favors the coalescence between group I and group II cracks. Parkins reported nucleation of small cracks between two adjacent cracks as a mechanism to bridge between the cracks in Stage 1b.20,24 

  • Group III: Cracks initiated in the cyclic plastic zone.

The group III intergranular cracks, the nucleated cracks close to the crack tip, were observed only in the presence of low R-ratio cycles. Therefore, the initiation of these cracks can be explained with the aid of the damage accumulation model with some modifications to fit the context of HpHSCC crack growth. According to Equation (7), the cyclic plastic zone size increases as ΔK increases. Therefore, a larger cyclic plastic zone formed under low R-ratio cycles allows the secondary cracks to become large enough to be easily visible. The HpHSCC crack propagation mechanism relies on the dissolution of the grain boundaries, and the cracks are intergranular in nature. If the accumulated strain were potent enough to fracture the metal, the cracks would be transgranular. Hence, this mechanism cannot be responsible for the crack propagation in the case of HpHSCC. However, the generated strain by such load fluctuation helps to form film-free conditions at the grain boundaries located in the cyclic plastic zone. The materials in this region experience stress well above the yield stress, as schematically shown in Figures 7 and 8. In this region, the accumulated strain leads to rupture of the passive film at the grain boundaries. The strain rate applied in this study was high enough to suppress the repassivation on the grain boundaries. Therefore, grains at the crack tip are under film-free conditions, and intergranular cracks initiate. These cracks are shown in Figure 5(c) and Figure 6(a) through (c). The observed increasing trend in crack density with increasing load cycle frequency is because of the higher strain rate generated at higher frequencies. The higher strain rate favors the film-free conditions by preventing repassivation.

  • Group IV: A single crack initiated from the precrack tip.

The group IV crack, an extension of the pre-existing crack, was observed in all of the samples to different extents, and is considered the main crack in this study. This crack is formed through either extension of the pre-existing crack tip on the surface or the merging of the secondary cracks and the main crack. One mechanism for the propagation of the existing crack is low-temperature creep. This mechanism can be applied to any of the nucleated cracks as well.34-35  Low-temperature creep is a phenomenon caused by high R-ratio loading cycles in the materials that develop strain hardening. When such material is loaded monotonically beyond the yield point, the interaction between the dislocations or dislocations and existing barriers, such as grain boundaries, increases the internal stresses. Therefore, an increase in applied stress is required for further strain, i.e., strain rate decreases. This behavior is known as strain hardening or work hardening. Nevertheless, this behavior might alter under cyclic loading conditions where the load is partially removed and then restored. During the unloading event, the glissile dislocations move backward because of back stresses from sessile dislocations. During the backward movement of these dislocations, cross slip or rearrangement of the dislocations can occur. Accordingly, the effects of work hardening are eliminated to some extent. At the onset of reloading, the mobile dislocations glide forward again and restore strain. The motion of dislocations and the resultant plastic strain continue unless the strain rate decreases by strain hardening again. Considering the dislocation network’s changes during the unloading, strain hardening is postponed to strains greater than the initial strain. Hence, each load cycle generates a strain increment. The strain caused by low-temperature creep is cumulative, yet the creep increment decreases progressively.18,54-56  Low-temperature creep has been proposed as the primary mechanism for the early stage of the HpHSCC crack growth.3  The strain generated by low-temperature creep can provide film-free conditions at the grain boundaries close to the precrack tip and can cause the crack length on the free surface to increase. The concept of low-temperature creep can be applied to the other nucleated cracks as well. However, the strain caused by low-temperature creep will be exhausted within 24 h.

The small secondary cracks near the main crack tip may merge to the predominant crack and elongate the crack on the surface. Any factor that increases the density of secondary cracks near the existing crack tip increases the possibility of crack coalescence. For example, low R-ratio cycles contribute to the crack propagation of the fourth group of the cracks through assisting nucleation of intergranular cracks near the main crack tip.

Crack Growth Behavior

Regardless of the crack’s relative location to the precrack tip, some points must be clarified. First, both initiation of new cracks and propagation of the existing cracks are controlled by anodic dissolution at the grain boundaries. Therefore, neither initiation of the crack nor propagation happens unless the mechanical driving force, i.e., sufficient strain rate to rupture the passive film on the grain boundaries, is provided. When this film is ruptured, the grain boundaries will be corroded, and intergranular cracks will initiate or propagate. However, the time frame over which the strain is provided is critical as well. When a given amount of strain is applied during a shorter time, i.e., at higher frequencies, the chance for repassivation on the grain boundaries decreases. Consequently, the dissolution of the grain boundary can proceed to either form or propagate the intergranular crack. As mentioned earlier, it can be hypothesized that there is a critical strain rate for crack initiation rather than a threshold stress. Second, large load fluctuations assist the nucleation of secondary cracks. Reduction in the R-ratio is accompanied by a decrease in threshold stress for crack initiation, based on the Parkins experiments on tapered specimens. Hence, the chance for crack nucleation increases under cyclic loading conditions. Third, low-temperature creep assists the propagation of both nucleated cracks and pre-existing cracks.

Figure 6 shows that the density of intergranular cracks increases as the frequency of the low R-ratio cycle increases. Assuming the same stress condition caused by cyclic loading with the R-ratio of 0.5, an increase in the frequency means an increase in the strain rate. Therefore, it can be postulated that there is a critical strain rate for cracking and a threshold for crack initiation. Further investigation that calculates the strain rate at the grain boundaries is needed to prove this hypothesis. It is suggested that future research should consider the characteristics of the grain boundaries, because statistics showed that the high-angle grain boundaries are more prone to cracking.57-58  This postulation should be a research topic for the future.

Among the above crack categories, group IV cracks are of most interest to this paper. As mentioned earlier, many of the nucleated cracks become dormant and do not grow. However, group IV represents growing cracks. If the geometrical evolution of such cracks continues, the threshold mechanical driving force for Stage 2 will be achieved at the crack tip. Additionally, the growth of group IV cracks increases the chance for coalescence, according to Equation (8). All of the crack growth rates are based on this group of cracks. The dimensions of Group IV can be measured on the fracture surface of the CT specimens. Figure 11 shows the fracture surfaces of the CT specimen tested under constant-amplitude loading waveforms. For small load fluctuation, such as R0.9_F5E-2, a tiny intergranular region forms between the fatigue precrack and lab fracture regions, as shown in Figure 11(a). The length of this region on the free surface is 24 μm. This intergranular crack is probably the extension of the existing crack because of low-temperature creep. No secondary crack initiation is evident on the fracture surface, which aligns with the metallographic observations (see Figure 5[a]). Figures 11(b) and (c) show the CT specimens’ fracture surfaces under R0.7_FE-2 and R0.5_FE-4 test conditions, respectively. Under these test conditions, the crack length on the free surface is higher than in the thickness direction, suggesting the occurrence of secondary crack coalescence and the extension of the pre-existing crack. Figures 11(d) and (e) shows the fracture surface of the CT specimens tested at R = 0.5 at frequencies of 10−3 Hz and 10−2 Hz, respectively. Crack coalescence is evident in both conditions. This observation is in accordance with Figure 6, which shows an increasing trend in the density of intergranular crack density at the cyclic plastic zone with increasing load cycle frequency. It can be concluded that large load cycles assist the crack propagation through the initiation and coalescence of secondary cracks in the cyclic plastic zone.

FIGURE 11.

SEM images of the fracture surfaces of CT specimens tested under constant-amplitude loading conditions: R-ratio of 0.9 and frequency of 5 × 10−2 Hz (a), R-ratio of 0.7 and frequency of 10−2 Hz (b), R-ratio of 0.5 and frequency of 10−4 Hz (c), R-ratio of 0.5 and frequency of 10−3 Hz (d), and R-ratio of 0.5 and frequency of 10−2 Hz (e).

FIGURE 11.

SEM images of the fracture surfaces of CT specimens tested under constant-amplitude loading conditions: R-ratio of 0.9 and frequency of 5 × 10−2 Hz (a), R-ratio of 0.7 and frequency of 10−2 Hz (b), R-ratio of 0.5 and frequency of 10−4 Hz (c), R-ratio of 0.5 and frequency of 10−3 Hz (d), and R-ratio of 0.5 and frequency of 10−2 Hz (e).

Figure 12 depicts the HpHSCC crack growth rates on the side faces of the CT specimens under different constant-amplitude loading conditions. The minimum crack growth rate was 8 × 10−9 mm/s and was obtained under the R0.9_5E-3 test condition, where the R-ratio was 0.9 and the frequency was 5 × 10−3 Hz. On the other hand, the R0.5_E-2 test condition yields the highest crack growth rate. According to Figure 12, the HpHSCC crack growth at Stage 1b is sensitive to the load cycles’ characteristics so that the maximum crack growth rate was found on CT specimens under the largest and most rapid load changes. Two significant trends are evident in the crack growth behaviors reported in Figure 12. First, the crack growth rate increases as the amplitude of load fluctuation increases, i.e., decreases in R-ratio. Secondly, the crack propagates faster at a higher frequency of cycling under the same R-ratio. These trends are in accordance with metallographic observations and fractographic examinations. Accordingly, the secondary cracks initiated in the cyclic plastic zone contribute to the crack propagation of a single crack at this stage.

FIGURE 12.

Variation of crack growth rates on the side faces of the CT specimens under different constant-amplitude loading scenarios.

FIGURE 12.

Variation of crack growth rates on the side faces of the CT specimens under different constant-amplitude loading scenarios.

IMPLICATIONS FOR PIPELINE OPERATORS

For pipelines vulnerable to HpHSCC, where environmental prerequisites for HpHSCC are established, intergranular cracks are most likely to initiate at metallurgical discontinuities. Although the maximum allowable hoop stress for the pipeline is less than 72% of the specified minimum yield strength, HpHSCC cracks can form at the metallurgical discontinuities where operating stress is intensified and can reach the yield stress. Other stress sources, such as residual stress, can add to the hoop stress locally and help provide the threshold stress for cracking. It has been shown herein that internal pressure fluctuations assist crack initiation. Cracks initiate at multiple sites. When the first intergranular cracks emerge on the surface of the pipe, they will act as stress risers. The neighboring area to the initiated crack, where the stress is intensified, is a breeding ground for secondary crack initiation. Similar to the initiation of the first crack, secondary crack initiation is facilitated by load fluctuations. In the presence of large load fluctuation, particularly high-frequency fluctuation, a high density of tiny secondary cracks forms close to the main crack tip. Then crack coalescence in this region causes the existing crack to propagate. According to Equation (8), the tendency for crack coalescence increases when the average length of two adjacent cracks increases. When two large cracks coalesce on the free surface, the mechanical driving force in the crack depth increases significantly. If Kdepth exceeds KISCC, Stage 2 of crack propagation starts where a crack propagates continuously through an anodic dissolution mechanism. It can be concluded that rapid and large load cycles have negative impacts on the pipeline lifetime. Therefore, controlling the pressure fluctuation to decrease either or both their amplitude and frequency will delay the onset of Stage 2, as shown in Figure 13. This illustration assumes that the crack nucleation and Stage 2 of HpHSCC crack growth are independent of load condition.

FIGURE 13.

Schematic illustration of the bathtub model under uncontrolled load fluctuation and controlled load fluctuation.

FIGURE 13.

Schematic illustration of the bathtub model under uncontrolled load fluctuation and controlled load fluctuation.

CONCLUSIONS

The effect of pressure fluctuations on HpHSCC crack growth behavior at Stage 1b (where Kmax < KISCC) were studied in an aqueous solution of 0.5 M Na2CO3 and 1 M NaHCO3 at 40°C and applied cathodic protection of −590 mVSCE. It was observed that the crack growth during Stage 1b is sensitive to the size of the load fluctuations and the cycling frequency. The main findings of this research are as follows:

  • This research was one of the first systematic studies on Stage 1b of HpHSCC crack growth. The current study provides insight into the fact that there are preferential regions for secondary crack initiation in Stage 1b. Hence, crack propagation in Stage 1b is not a random process and depends on loading characteristics and existing cracks.

  • A number of intergranular cracks initiate in the plastic zone of pre-existing cracks. Intensified stress in this zone ruptures the passive film at the grain boundaries, and some of the grain boundaries persist in film-free conditions. Anodic dissolution at these bare grain boundaries causes the formation of intergranular cracks. The intergranular cracks can be classified into four groups based on their relative distance from the pre-existing crack tip, viz. cracks initiated at the boundary of the actual plastic zone, cracks nucleated in the theoretical plastic zone, cracks nucleated in the cyclic plastic zone, and cracks nucleated at or ahead of the pre-existing crack.

  • Large load fluctuations generate a cyclic plastic zone at the crack tip. The cumulative strain is developed in this region. Depending on the strain rate, film-free conditions are formed on the grain boundaries located in this region. Therefore, the intergranular crack density in the cyclic plastic zone is comparatively higher than in the other zones. These tiny cracks are close to the main crack tip; therefore, these cracks can coalesce to the main crack easily and cause the pre-existing crack to propagate.

  • Increasing the length of individual cracks increases the chance for large crack coalescence accompanied by an acceleration of the onset of Stage 2.

  • The crack initiation dependency on the frequency of the load cycles suggests there is a critical strain rate rather than just a threshold stress for crack initiation. Further investigations that consider grain boundary characteristics, strain distribution, and localized strain rates at the grain boundaries within the plastic zone are suggested to prove this postulate.

Trade name.

ACKNOWLEDGMENTS

The authors thank TC Energy, Enbridge Pipelines Inc., Natural Science and Engineering Research Council of Canada, and Pipeline Research Council International for financial support.

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