The electrochemical nature of stress corrosion cracking

The electrochemical nature of stress corrosion cracking

6

D.D. Macdonald University of California at Berkeley, Berkeley, CA, United States

6.1

Introduction

The stress corrosion cracking (SCC) of metals and alloys in aqueous environments is a classic example of localized corrosion that falls within the differential aeration hypothesis (DAH) [1]. Cracking in sensitized type 304 boiling water reactor (BWR) primary coolant (water at 288
C) is purely intergranular and is referred to as intergranular SCC (IGSCC). IGSCC is a major threat to the structural integrity of the primary coolant circuits of second-generation BWRs; in retrospect, the problem reflects a poor initial choice of materials, but it is a problem that each BWR operator, except those in Germany (because of the use of a stabilized grade of stainless steel (SS)), must deal with. It is, therefore, essential that the origin of IGSCC in sensitized type 304 SS be understood and the relationship between crack growth rate (CGR) and the properties of the coolant be accurately defined. A schematic of a BWR is displayed in Fig. 6.1(a). A BWR uses the heat of nuclear fission to boil water in the core; the resulting water and steam are separated, and the steam is dried. The dry steam is then sent to the turbines to generate electrical energy. As the steam expands through the turbines it cools, and at the exit of the low-pressure steam turbine the temperature is typically 95
C. The steam is then condensed and returned to the reactor. The water in the core that was not converted to steam is recirculated to the core via the recirculation piping system for thermohydraulic reasons (Fig. 6.1(b)). It is within this recirculation system that IGSCC in the heat-affected zones adjacent to welds in the steel was first observed in the 1970s. Since that time, the “disease” has spread to the internal components of the reactor pressure vessel, such as the core shroud, jet pump hold-down beams, safe ends, and other components. As the water passes through the core, it is subject to radiolysis by neutrons and g-photons, producing a variety of electroactive products including O2, H2O2, H2, H, OH, and O2  e(aq) [2]. Of these species, only O2, H2O2, and H2 are present in the coolant at concentrations sufficient enough to affect the electrochemistry of the circuit, as reflected by the redox potential and the electrochemical corrosion potential (ECP) of the steel. Extensive modeling of the primary coolant circuits of BWRs [2] shows that the corrosion potentials of most, if not all, components in the primary circuit are generally above the critical potential for IGSCC (Ecrit), implying that all of these components are in a perpetual state of cracking. The material challenges that exist in developing water-cooled nuclear power reactors have been comprehensively reviewed by Zinkle and Was [3], who also comment Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors http://dx.doi.org/10.1016/B978-0-08-100049-6.00006-9 Copyright © 2016 European Federation of Corrosion. Published by Elsevier Ltd. All rights reserved.

240

(a) Reactor building

(b)

Boiling water reactor system

Vent and head spray

Steam dryer lifting lug

(secondary containment) Inerted drywell (primary containment) Turbine generators

Reactor core

Electricity to switch yard

Steam dryer assembly

Steam outlet

Steam separator assembly

Reactor pressure vessel

Feedwater inlet (nozzle)

Core spray inlet

Feedwater sparger

Control rods

Feedwater pumps

Condenser

Low pressure coolant injection inlet

Core spray line

Jet pumps (beams)

Torus

Top guide Fuel assemblies

Recirculation intel (piping)

Core shroud Control blade (absorber tubes) Recirculation outlet

Manifold (piping)

Recirculation pump motor Shutoff valve

Bypass line

Shutoff valve

Recirculation pump

Key components of the BWR. the parts names in red indicates areas of IGSCC.

Figure 6.1 Schematic of a boiling water (nuclear) reactor (a) and a cut-away view of the reactor pressure vessel (RPV) and the RPV internals (b).

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

Main steam lines

The electrochemical nature of stress corrosion cracking

241

on the numerous methods that have been explored to mitigate this problem. These methods including stress relief, low conductivity operation, hydrogen water chemistry (HWC), and changes to materials, to name a few of the more prominent approaches. Of these, only HWC [4] has shown promise in existing plants, although the ultimate solution for new plants is to use a stabilized grade of SS (eg, type 347), a low-carbon grade (type 304L), or a nitrogen-strengthened, low-carbon grade (type 304NG) that do not sensitize upon welding. In this regard, it is important to note that type 347 SS has been used in German BWRs since the 1960s, and there has never been an incident of IGSCC in those reactors. To understand the problem of IGSCC in sensitized type 304 SS in BWR primary coolant environments, it is necessary to understand the role of not only water chemistry [4] but also electrochemistry [2], because the latter establishes the ECP, which is the most important parameter in determining the susceptibility of a steel to cracking. The material within which IGSCC is observed in US-designed BWRs is AISI type 304 SS, containing more than 0.02 wt% carbon (typically 0.08 wt%), which renders the steel susceptible to thermal sensitization upon welding [5]. In thermal sensitization, zones affected by weld heat on either side of a weld experience a temperature decay that passes through the range of 800e500
C as the weld solidifies and the matrix cools, and it is within this range that carbon reacts with chromium to form C23C6 precipitates on the grain boundaries. The formation of these precipitates denudes the adjacent grain boundary matrix of chromium, and the chromium concentration is found to decrease below the 11 wt% that maintains the steel “stainless.” Thus the steel becomes a composite structure comprising SS grains that are glued together with low-chromium grain boundary matrices. Stressassisted grain boundary corrosion occurs around the grains to yield the intergranular or “crystalline” structure that is typical of IGSCC (Fig. 6.2). The carbide precipitates are readily redissolved by solution annealing at a temperature of

720X

20 μm

Figure 6.2 Typical micrograph of intergranular stress corrosion cracking in the heat-affected zone of thermally sensitized type 304 stainless steel. Note that cracks are observed to nucleate on both emergent grain boundaries and on pits that are not apparently associated with emergent grain boundaries.

242

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

1050
C for about 1 h, followed by a water quench, to restore the unsensitized state. However, while this procedure is practical in treating shop welds, it is generally impractical for desensitizing welds in the field. An important feature of the DAH is that the local anode and the local cathode are spatially separated, with the former existing within the crack enclave (including on the crack flanks and crack tip) and the latter existing on the bold, external surfaces, which have the greatest access to the cathodic depolarizer (eg, oxygen) [2] (Fig. 6.3). Because of the need to compensate the positive charge being deposited into the crack enclave from metal dissolution, anions (eg, Cl) are transported into the cavitydprocesses that are manifest as a positive current flowing from the crack to the external surfaces, where the current is consumed by the reduction of hydrogen ions, water, oxygen, and/or H2O2 (Fig. 6.3). It is evident, therefore, that the crack internal and external environments are strongly coupled, as noted above, and hence that the properties of the Fluid flow Oxygen transport

Positive current

Positive current

O2 + 4H+ + 4e– → 2H2O

Electron current

φ Ls

Net positive current

O2 + 4H+ + 4e– → 2H2O

φ ∞s

Electron current

Crack advance

Figure 6.3 Schematic of the differential aeration hypothesis, which is the basis of localized corrosion and the coupled environment fracture model. The coupling current is required by the differential aeration hypothesis for localized corrosion, and the conservation of charge requires that the electron current flowing from the crack to the external surface must be equal to the positive ionic current flowing through the solution from the crack to the external surface, and that the two currents must be annihilated at the external surface via a charge transfer reaction. D.D. Macdonald, M. Urquidi-Macdonald, Corros. Sci. 32 (1991) 51.

The electrochemical nature of stress corrosion cracking

243

external environment must be taken into account when modeling SCC [6e10]. Thus it must be emphasized once again that the local anode and the local cathode are spatially separated, as depicted in Fig. 6.3, with charge conservation dictating that a positive ion current flows from the crack to the external surfaces, and that this current must be balanced by the electron current flowing through the metal in the same direction. Because these currents are annihilated at the external surface via a charge transfer reaction (eg, oxygen reduction), it is evident that the kinetics of this charge transfer reaction must be instrumental in determining the CGR. The electron current is known as the “coupling current,” which is easily measured (see later). It is argued below that not only must the origin of the coupling current be understood to discern the mechanism of SCC, but that it provides an unrivaled tool for examining the processes that occur at the crack tip [6e11]. As noted above, coupling of the internal and external environments of a localized corrosion event (pit, crevice, or crack) is required by the DAH in order for the system to conserve charge. Importantly, this current also ensures that a suitably aggressive environment is maintained within the cavity, such that repassivation of the crack tip is inhibited and that localized attack continues. The environment at the crack tip is aggressive because metal ion hydrolysis produces Hþ and because of the accumulation of anions, such as chloride ions; as a result, the crack enclave contains essentially concentrated hydrochloric acid (see later). Because the strength of the coupling between the internal and external environments is reflected in the magnitude of the coupling current, characterization of the coupling current is of vital importance in developing robust, predictive models for the evolution of localized corrosion damage, including SCC, as noted above. The DAH, which was first formulated in 1923 by Evans [1], dictates that localized corrosion occurs only so long as the system is able to maintain a spatial separation between a local anode and a local cathode, and hence is able to maintain the crack tip in a semi-depassivated state by maintaining high local concentrations of Hþ and Cl. If differential aeration cannot be maintained, the cavity “dies” (repassivates) and SCC ceases, as has been demonstrated experimentally by coating the external surfaces with an insulator (eg, ZrO2), which inhibits the oxygen reduction reaction [11]. (Actually, in this case, differential aeration was never established, and hence IGSCC did not initiate in the coated specimen, but it did initiate in a daisy-chained, uncoated specimen). The DAH, which has stood the test of time for more than 90 years, is the basis of various “coupled environment” models, including the coupled environment fracture model (CEFM), developed by Macdonald and his colleagues [6e10] over the past two decades. In this chapter some aspects of the electrochemistry of SCC and, in particular, of coupling between the internal and external environments of systems undergoing environment-assisted cracking (EAC) are reviewed, with emphasis on the IGSCC of sensitized type 304 SS in high-temperature aqueous environments that are prototypical of the primary coolants in BWRs. The origin of the coupling current is examined in depth, and the mechanistic implications of the noise in the coupling current for SCC are explored. It is argued that the coupling current not only contains valuable mechanistic information, but that, in one case at least (IGSCC in sensitized type 304 SS in high-temperature aqueous solutions), the mean current varies linearly with CGR.

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Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

This latter relationship implies that measurement of the coupling current may also represent an extraordinarily sensitive means of determining CGR down to the creep CGR limit. Finally, the chapter also explores the dependence of CGR on the electrochemical crack length (ECL), and it is argued that this relationship accounts for the development of elliptical surface cracks and for the convex shape of the crack front in C(T) specimens as viewed from aft of the crack front, when the crack propagates under environmental control. While the chapter emphasizes IGSCC in a sensitized SS, the principles that are explored are perfectly general and can be used to describe SCC in other alloy/environment systems.

6.2

Critical potential

As noted above, a key to developing electrochemical methods for controlling EAC in reactor coolant circuit materials was the observation of a critical potential for crack propagation in sensitized type 304 SS in high-temperature aqueous solutions [12,13]. Thus, earlier and subsequent work has demonstrated that most, if not all, localized corrosion processes, including pitting corrosion, SCC, corrosion fatigue, crevice corrosion, hydrogen-induced cracking (HIC), and erosion-corrosion (E-C), exhibit critical potentials. In each of these cases, there exists an “electrochemical switch” such that the corrosion process occurs at potentials greater than (or less than, in the case of HIC and E-C of carbon steel in high-temperature water) the critical value, but not at potential values less than (or greater than for HIC and E-C) the critical value. In the case of IGSCC in sensitized type 304 SS in high-temperature aqueous solutions, the critical potential is most commonly determined using constant extension rate experiments, in which smooth, round tensile specimens were strained to failure at a constant strain rate (typically 105 to 107 s1) while controlling the ECP electronically (using a potentiostat) [12,13]. The principal criticism of this type of experiment is that it is not only severe, and may indicate cracking in the laboratory where no cracking may occur in the field, but that a positive result (IGSCC) may in fact indicate electrochemical control over the initiation event and not necessarily over crack propagation. However, this latter issue was resolved by demonstrating that after the crack was initiated (ie, during the propagation stage), and hence when the load relaxed under constant displacement conditions, the crack (as indicated by the relaxing load) could be arrested, by displacing the potential in the negative direction, or accelerated by displacing the potential in the positive direction, corresponding to switching the crack “off” or “on,” respectively. Since that time, numerous works have demonstrated, using fracture mechanics (C(T)) specimens, that the CGR is a strong positive function of the corrosion potential, as measured on the external surface, and that there exists a critical potential (Ecrit) of about 0.23 Vshe (volts on the standard hydrogen electrode scale) below which IGSCC is not observed [12,13] (Fig. 6.4). At more negative potentials, the CGR is independent of ECP, and hence of the electrochemistry of the system, with the mechanism of crack advance being dominated by creep. It should be noted, however, that the critical potential depends on a variety of factors, including temperature,

The electrochemical nature of stress corrosion cracking

245

Experimental data [16] 0.1 μS/cm - Ford’s correlation [16]

10–6

0.5 μS/cm - Ford’s correlation [16] 0.1 μS/cm - Congleton’s correlation [17] 0.5 μS/cm - Congleton’s correlation [17] 0.1 μS/cm - Ford/Andresen [16]

Crack propagation rate (cm/s)

0.2 μS/cm - Ford/Andresen [16]

10–7

κ = 0.3 κ = 0.2 κ = 0.1 (μS/cm)

0.3 μS/cm - Ford/Andresen [16]

304 stainless steel 25 mm CT specimen

10–8

288°C water constant load Assumed condition 25 ksi-in1/2 (27.5 MPa √m)

10–9

Observed data 0.1–0.3 μS/cm 15 C/cm2

Calibration datum

10–10

–0.8

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

Corrosion potential (Vshe)

Figure 6.4 Measured (data points) and calculated (via the coupled environment fracture model (CEFM); curves) crack growth rates for sensitized type 304 stainless steel in high-temperature aqueous solutions as a function of the electrochemical corrosion potential and conductivity. The citations refer to references in the original source. The CEFM was calibrated on the single datum indicated in the figure. D.D. Macdonald, P.C. Lu, M. Urquidi-Macdonald, T.K. Yeh, Corrosion 52 (1996) 768.

the degree of sensitization (DoS) of the steel, the extent of cold work, solution composition (including pH), and the ECL, so that it is a mistake to regard it as being a fixed system property. Indeed, experiments have shown that the critical potential for SCC in sensitized type 304 SS in high-temperature water may vary from about 0.1 to 0.45 Vshe, depending upon the exact conditions of the system [12,13]. The dependence of the critical potential on crack length is discussed at some length later in this chapter. These are important issues because the US Nuclear Regulatory Commission has sanctioned a value of 0.23 Vshe for SCC in operating BWRs. It has been argued that a more prudent approach would have been to define a critical CGR (eg, 109 cm/s, corresponding to a crack extension of about 0.012 in./year) [2], but of course CGR is more difficult to measure in an operating plant than is the ECP. It is important to note that this electrochemical switch is strictly not an “on/off” (bistable) switch, but rather displays a quasi-exponential or sigmoidal transfer function, with the lower limit corresponding to the creep rate (Fig. 6.4). Thus the critical potential corresponds to the lowest observable CGR at which the occurrence of environmentally induced, intergranular brittle fracture is negligible compared with ductile fracture; this is on the order of 1e2  1010 cm/s under favorable conditions

246

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

(Fig. 6.4). The requirement that the extent of intergranular fracture be negligible is tantamount to specifying a minimum coupling current, because theory [6e10] and experiments [14] show that the CGR is proportional to the coupling current, which in turn is a strong function of the potential at the external surface remote from the crack (ie, the ECP; Fig. 6.4; also see later). The fundamental origin of the critical potential for IGSCC is best illustrated by reference to Fig. 6.3. This figure illustrates schematically the fact that SCC, being a localized corrosion process, must be described within the framework of the DAH. Briefly, a viable crevice (crack) requires the separation of the local anode (in the crack) and the local cathode (predominantly on the external surface adjacent to the crack). This separation, which occurs principally for geometric reasons, results in, and is maintained by, the flow of positive current through the solution from the crack to the external surface, balanced by electron flow through the metal in the same direction, as indicated in Fig. 6.3. The part of the current that is generated at the crack tip (as opposed to that generated on the crack flanks) contributes directly to the propagation of the crack through, for example, the electrodissolution of the crack tip matrix and/or injection of hydrogen into the matrix ahead of the crack tip, as described by Faraday’s law and the appropriate crack advance mechanism. However, all of the current, whether it originates at the crack tip or the crack flanks, contributes to maintaining aggressive conditions within the crack enclave (ie, by low pH and high [Cl]). As we will see later in this chapter, the pH is predicted to be as low as 0 and the concentration factor for chloride is predicted to exceed 106, provided that the concentration of chloride in the bulk environment is sufficiently low. Accordingly, the crack tip environment is essentially concentrated HCl, which inhibits repassivation of the crack tip and thereby ensures that the crack tip remains active, as previously noted. In the case shown in Fig. 6.5, which was modeled using the CEFM [6e10], crack advance is attributed to coupled slip/dissolution/repassivation (SDR)eHIC, with the result that the CGR is directly proportional to the coupling current, as demonstrated experimentally [14], except when the potential is sufficiently negative that creep crack growth becomes the controlling factor. Accordingly, noting that maintenance of sufficiently aggressive conditions in the crack for IGSCC to occur is the result of the electromigration of anions (eg, Cl) into the crack, coupled with the hydrolysis of cations released at the crack tip and flanks, and that these processes are contradicted by diffusion of Hþ and Cl out of the crack because of the establishment of concentration gradients, it is evident that there must exist a minimum coupling current below which IGSCC is negligible compared with the creep rate (purely mechanical fracture). Thus the critical potential can be identified, with the potential at the external surface, at which the coupling current no longer ensures sufficient separation between the local anode in the crack and the local cathode on the external surface under the loading conditions applied. For the case modeled in Fig. 6.5, the critical coupling current appears to be on the order of 0.5 nA. The reader is cautioned, however, that this current density should be regarded as being little more than a rough estimate, and that it will surely be revised as more sophisticated models are developed and as more accurate and extensive experimental data become available.

The electrochemical nature of stress corrosion cracking

247

Crack growth rate (cm/s) or coupling current (A)

10–5 10–6

Crack growth rate Coupling current

10–7 10–8 10–9 10–10 –0.6

–0.4

–0.2

0.0

0.2

0.4

0.6

Corrosion potential vs SHE/V

Figure 6.5 Calculated crack growth rate and coupling current for intergranular stress corrosion cracking in sensitized (degree of sensitization, 15 C/cm2) type 304 stainless steel in diluted NaCl solution (0.135 ppm Na) at 288
C as a function of potential of the steel at the external surfaces remote from the crack mouth (the electrochemical corrosion potential) and as modeled using the coupled environment fracture model [2e7]. Stress intensity factor KI ¼ 27 MPa Om, crack length ¼ 0.5 cm, crack width ¼ 1.0 cm, crack mouth opening displacement ¼ 5  104 cm, solution flow velocity ¼ 100 cm/s, hydrodynamic diameter ¼ 50 cm, solution conductivity k25 ¼ 0.807 mS/cm, k288 ¼ 6.89 mS/cm, and pH at 288
C ¼ 5.89 (k25, k288, and pH at 288
C correspond to the bulk solution) [15]. SHE/V.

6.3

Coupling of the internal/external environments

The applicability of the DAH in accounting for SCC has been demonstrated experimentally by Manahan et al. [16] and by Wuensche and Macdonald [14] by measuring the coupling current during IGSCC in type 304 SS in high-temperature water (simulated BWR coolant at 288
C), and more recently by Liu and Macdonald [17] and Gomez-Duran and Macdonald [18,19], who monitored the coupling current during the fracture of AISI 4340 steel in caustic solutions at 70
C and the intergranular fracture of sensitized type 304 SS in thiosulfate solutions at an ambient temperature (22
C), respectively. The coupling current was monitored in all four studies by coating C(T) specimens with polytetrafluoroethylene so as to inhibit the cathodic reactions that normally occur on the external surface. The coupling then was measured by using a sensitive zero-resistance ammeter (ZRA) connecting the specimen and cathodes of the same material as the specimens mounted on the specimen sides in close proximity to the crack [16e19] (Fig. 6.6). Provided that the side cathodes are sufficiently close to the crack, they act as the “external surface,” with the current being routed through the ZRA, where it is measured, rather than flowing directly from the crack tip and flanks to the external surface (Fig. 6.3). The ZRA ensures that the cathodes are at the same electrostatic potential as the specimen, a condition that would exist if the specimen and the cathodes were contiguous. In all four cases the coupling current was found to contain information that

248

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

1.1 × 10–6 1.1 × 10–6 1.1 × 10–6 10–6 9.5 × 10–7

–6

–6

1.

8

×

10

10

–6

6 1.

×

4

×

10

–6

10 1.

× 2

–7

–6

10 1.

×

× 0 8.

0

10

10

–7

10 0 4.

×

0 2.

×

10

–7

8.5 × 10–7

–7

9.0 × 10–7

6.

Crack growth rate (cm/s)

1.2 × 10–6

Coupling current (μA)

Figure 6.6 Experimentally determined relationship between the crack growth rate and coupling current for intergranular stress corrosion cracking in sensitized type 304 stainless steel in oxygenated (7.6 ppm, 2.38  104 m) sodium chloride (50 ppm, 8.62  104 m) solution at 250
C [14]. This same linear dependence of the coupling current on crack growth rate is predicted by the coupled environment fracture model.

led to a reassessment of the fundamental mechanisms of EAC, particularly with respect to the processes that occur at the crack tip. Briefly, the data are inconsistent with a pure SDR model for crack advance, as has been assumed in the past (without significant experimental support) [20]; instead, they suggest that cracks advance in the materials and under the conditions used in these studies by periodic hydrogen-induced fracture [21e24]. This finding, together with the demonstrated role played by the external surfaces, required a fundamental reassessment of the mechanism of crack advance and of the roles played by the various processes involved. A typical coupling current versus time plot for IGSCC in type 304 SS, obtained using a platinized nickel side cathode (in some experiments, cathodes of different types were used, with only one being connected to the ZRA at any given time), as the load and hence the stress intensity is stepped to successively higher values [15,16] (Fig. 6.7). It was found that no coupling current flowed until the stress intensity factor exceeded 11 MPa Om, but thereafter the coupling current increased rapidly with increasing stress intensity (KI) to saturate at about 500 mA and a KI value of 33 MPa Om. While it is tempting to identify KISCC with a value between 11 and 22 MPa Om, it is possible that the lack of coupling current at low loads (low KI values) simply reflects the existence of an induction time for the penetration of the crack through the fatigue-induced plastic zone ahead of the crack tip (the specimen was fatigue precracked), and hence that the true value of KISCC is significantly lower. It should be noted again that this particular experiment used a platinum (Pt)-catalyzed side cathode because of a concern before the experiment that the coupling current would be very small (on the order of a few nano-amperes) and hence might be difficult to measure accurately. Thus it was postulated that catalysis of the oxygen reduction reaction would substantially increase the coupling current and hence make it easier

The electrochemical nature of stress corrosion cracking

249

Water temperature = 280°C Pressure = 82.7 bar KI = 44 MPa √m

1200 Load

KI = 33 MPa √m

1000

700 600

Load (kg)

400 KI = 22 MPa √m

600

300 200

400 KI = 11 MPa √m

100

200 0 0.00

ZRA current (μA)

500 800

0 –100 0.50

1.00

1.50

2.00 Time (h)

2.50

3.00

3.50

Figure 6.7 Plot of the coupling current (CC) and stress intensity (KI) versus time for intergranular stress corrosion cracking in sensitized type 304 stainless steel in high-temperature (288
C) water as the load is stepped periodically [12]. Note that the mean CC is a high fraction of the fluctuation amplitude, indicating that the current arises primarily from crevice corrosion [15]. ZRA, Zero-resistance ammeter. M.P. Manahan Sr., D.D. Macdonald, A.J. Peterson Jr., Corros. Sci. 37 (1995) 189.

to detect, as observed (the coupling current for this case is approximately 50 times greater than that observed with type 304 SS side cathodes; see later). These data demonstrate unequivocally that the coupling current is a sensitive function of the kinetics of oxygen reduction on the surfaces external to the crack, confirming one of the more important predictions of the CEFM. Inhibition of the oxygen reduction reaction is also predicted to have a profound impact on the coupling current and on the CGR, and this prediction has been confirmed experimentally [11]. Further note that upon unloading, the coupling current drops to zero, an observation that can be attributed to crack closure (although a small negative current flows because of galvanic coupling between the steel specimen and the Pt-catalyzed nickel cathode). At higher loads (higher KI values), the mean of the coupling current is clearly much larger than the amplitude of the fluctuations, suggesting that the coupling current comprises two components: one component from the periodic fracture at the crack tip (the fluctuating component), and the other a time-independent component arising from crevice corrosion. Thus, the lack of a coupling current comprising either or both components for KI <11 MPa Om suggests that neither crack advance nor crevice corrosion is occurring in the system. The lack of a coupling current and hence of crack advance is simply due to the lack of periodic fracture at the crack tip and to crack closure. Upon recording the coupling current at a sufficiently high acquisition frequency (100 Hz) under the conditions described in Fig. 6.7, a remarkable noise structure is revealed (Fig. 6.8). The noise comprises packages of periodic oscillations; the number of oscillations in each package ranges from 4 to about 13, and each package is

250

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors Water temperature = 288°C Pressure = 82.7 bar 100

1100 1000

90

Load (kg)

Acquisition rate 100 Hz

80

KI = 33 MPa √m

800

70

700

60

600

50

500

40

400

30

300

20

200

10

100

0

ZRA current (μA)

Load

900

–10

0 0

5

10

15 Time (s)

20

25

30

Figure 6.8 Typical form of the noise in the coupling current (CC) for type 304 stainless steel with two type 304 stainless steel side cathodes in simulated boiling water reactor coolant at 250
C and at a stress intensity of 27.5 MPa Om [12]. Note that in this case the mean of the CC is approximately the mean of the fluctuations, demonstrating that, with uncatalyzed cathodes, the CC is overwhelmingly determined by the periodic fracture processes that occur at the crack tip. ZRA, zero-resistance ammeter. M.P. Manahan Sr., D.D. Macdonald, A.J. Peterson Jr., Corros. Sci. 37 (1995) 189.

separated by brief periods of intense but low-amplitude activity. Furthermore, the frequency of the periodic fluctuations in the coupling current changed reproducibly with variations in the stress intensity (Fig. 6.9) and, interestingly, no clear dependence of the frequency on cathode type (titanium vs type 304 SS) was observed, indicating

Microfracture event frequency (s–1)

2.5 2.0 1.5 1.0 0.5 0.0

0

10

20

30

40

50

60

Stress intensity, Kl (MPa √m)

Figure 6.9 Frequency of the brittle microfracture events versus stress intensity factor for intergranular stress corrosion cracking in sensitized type 304 stainless steel in water at 288
C (conductivity at 25
C ¼ 0.5e1.3 mS/cm; [O2] ¼ 0.15  103 m) [16].

The electrochemical nature of stress corrosion cracking

251

that the microfracture frequency is determined by the crack tip strain rate rather than processes that occur in the external environment. When the Pt-catalyzed cathodes were used, the amplitude of the noise in the coupling current was only about 10% of the total, the mean of which was between 500 and 600 mA, depending on the value of the stress intensity factor within the stage II region. The same noise amplitude is observed when using uncatalyzed type 304 SS cathodes, but now the mean coupling current is reduced to about 5 mA (Fig. 6.8), and no “direct current” component resulting from crevice corrosion is evident. This demonstrates that the principal role of the external surfaces is to support a greater coupling current in the catalyzed case compared with the uncatalyzed case, which in turn leads to a more aggressive environment within the crack and hence to a higher CGR. Yeh and Macdonald [25] confirmed the impact of catalysis of the redox reactions on the external surface on the CGR. Likewise, the CEFM predicts that inhibition of the redox reactions will decrease the CGR; that prediction was confirmed experimentally [11]. In the catalysis case, however, the additional current does not originate from the crack tip, but originates from the crack flanks, presumably reflecting the more aggressive conditions (lower pH and higher [Cl]) in the crack. Also of interest in this regard is the lack of any systematic dependence of the microfracture event frequency on the cathode material (Fig. 6.9), suggesting that the frequency is determined by the crack tip strain rate and the fracture strain, not by the kinetics of the charge transfer reactions occurring on the external surface. An interesting observation that can be made upon closely examining Fig. 6.8 is that current reversal occurs within the oscillations, particularly toward the left side of the plot. This implies momentary reversal of differential aeration, with the crack becoming the cathode and the external surfaces acting as the anode. During the brief time of reversal, hydrogen evolution within the crack enclave presumably acts as the cathodic reaction, and passive metal dissolution corresponds to the partial anodic process. To my knowledge, this is the first time that this phenomenon has been reported, and its fundamental origin is presently unknown. Because cracking is a dynamic process, the origin of the observed current reversal is possibly best described in terms of stability theory. The data presented in Fig. 6.9 are reproduced from Ref. [16]. Note that the plot is reminiscent of a plot of CGR versus stress intensity, suggesting that the effect of loading (stress intensity factor) on the CGR is primarily determined by the frequency of the microfracture events, rather than by the microfracture dimension (which is found to be only weakly dependent on KI, as argued later in this chapter). Also, no noise (or coupling current) was observed at very low stress intensity values (ie, for KI < KISCC). The observed relationship between the noise and the experimental independent variables (eg, KI) is such that the fluctuations in the coupling current most likely arise from brittle microfracture events occurring at the crack tip. Thus, upon examination of the noise [16], it was evident that the majority of the coupling current arises from the crack tip, whereas when highly catalyzed cathodes are used it, is apparent that the majority of the coupling current arises from the crack flanks, presumably in the neighborhood of the crack tip (see Ref. [10]), as noted above, but reflecting a dominance of crevice corrosion. This is a clear demonstration of the profound impact that the external surfaces, in their ability to annihilate the positive current exiting

252

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

the crack mouth, have on the processes that occur within the crack. It also provides unequivocal evidence of the need to consider processes that occur on the external surfaces when modeling EAC, as is done in the CEFM [6e10] (as noted elsewhere in this chapter), but which is not incorporated in any other model. As emphasized elsewhere in this chapter, the form of the noise in the coupling current has profound implications for the fracture mechanism. Thus, the fact that distinct, periodic fluctuations are observed demonstrates that, in this particular system, fracture occurs event by event across the crack front. This conclusion is reasonable because if many events of random frequency and phase occurred more or less simultaneously, then pseudo “white” noise should be observed across the entire time record. Finally, analysis of the noise [16] shows that, within each packet, the crack advances in discrete increments of 2e3 mm if it is assumed that the fracture events are semicircular, and by 0.24 mm if the event extends across the 30-mm average grain. Assuming that the event represents the advance of the crack across a grain face, it is apparent that each packet of events shown in Fig. 6.8 results in an extension of the crack by 8 mm (4  2 mm) to about 26 mm (13  2 mm). This may be compared with the grain size of 10 to 50 mm. On the other hand, if the crack advances across the grain width, on average 127 events should be observed in each package, rather than the 4 to 13 shown in Fig. 6.5. Thus the occurrence of semicircular brittle fracture events is indicative of a mechanism that involves the diffusion of a causative agent from a source at the crack tip into the matrix ahead of the crack, that is, of an HIC component. In analyzing the noise data, note that for a semicircular microfracture event of radius r occurring on a crack front of length B, B/2r events must occur, on average, for the crack to advance by the distance r. Accordingly, the CGR can be written as da 2r 2 f ¼ dt B

[6.1]

where B is the thickness of the specimen and f is the microfracture event frequency. Hence, by rearrangement, the event size becomes
r¼

 Bðda=dtÞ 1=2 2f

[6.2]

Since we know B (1.27 cm), can determine f (¼ 2 s1) from the noise (Fig. 6.7), and can measure da/dt (da/dt ¼ 2  107 cm/s, corresponding to an ECP of 0 Vshe; Fig. 6.4), we are able to determine the microfracture event size as r ¼ 2  3 mm [12]. A “back-of-the-envelope” estimate of r may be identified with the diffusion length for hydrogen in SS using the expression r ¼ ðD=f Þ1=2 , where D is the diffusivity and f is the microfracture event frequency. Taking D ¼ 1  107 cm2/s [26] and f ¼ 2 s1 (Fig. 6.9), we find r ¼ 2.2 mm. This value is in excellent agreement with the value derived from the noise in the coupling current, giving credence to the postulate that the fracture in sensitized type 304 SS in high-temperature water is essentially an example of HIC. This conclusion agrees with that of Briant [24], who also

The electrochemical nature of stress corrosion cracking

253

found that IGSCC in sensitized type 304 SS was due to HIC, and is in concert with other models of HIC [21e23]. It is, however, important to point out that, in reality, the findings discussed above demonstrate only that the matrix ahead of the crack tip is embrittled, which might also be accounted for by dealloying [27e29]. It is important to note that if fracture occurred via the classical SDR mechanism alone (ie, in the absence of embrittlement of the matrix ahead of the crack tip), the expected fracture dimension should be some small multiple of the Burgers vector for the slip system, and hence should be fractions of a nanometer, not micrometers, in size. The corresponding fracture frequency for the SDR mechanism should be in the kilohertz range to account for the observed CGR, not in the observed Hertz range. The inescapable conclusion is that the classical SDR mechanism [19] is incapable of accounting for the observed data and should be discarded. Similar experiments on other systems have been carried out in my laboratory, namely, cracking in AISI 4340 steel in caustic solution [17] and IGSCC in sensitized type 304 SS in contact with thiosulfate-containing solution [18,19]. In the case of fracture in tempered martensitic AISI 4340 steel in concentrated sodium hydroxide solution (6 M) at 70
C, which is a well-known case of HIC, the microfracture event dimension (49 mm) is on the order of the prior austenite grain size, and individual events are readily resolved in the time domain (Fig. 6.10(a)) by carefully selecting the temperature and the caustic concentration. (In more concentrated NaOH (eg, 7 M), it is evident that many microfracture events occur more or less simultaneously, giving rise to noise that is not readily deconvolved in the time domain. At lower NaOH concentrations (eg, 5 M), no microfracture events were detected and HIC did not occur [17].) Furthermore, a first-order kinetic plot yields the rate constant for repassivation of the fracture event (Fig. 6.10(b)), but the rate constant for repassivation was found to depend strongly on the orientation of the specimen with respect to the rolling direction of the steel, with that for the L-T orientation (k ¼ 0.000257 s1) being 100 times smaller than that for the S-L direction (k ¼ 0.029 s1), which indicates an interesting material/electrochemistry coupling that has never previously been described. Note that the transients shown in Fig. 6.8 and those shown in Fig. 6.10(a) are ostensibly different in form, but it should be remembered that the form of the transient strongly depends on the nature of the impedances in the rest of the circuit, including that at the external surface, where the coupling current is annihilated by the electron current flowing from the crack tip. If this impedance is highly reactive, as in the case of Pt and SS, the transients are expected to have the semisinusoidal appearance evident in Fig. 6.8 because of a relaxation at the leading edge of each event, whereas if the external impedance has low reactance, the form shown in Fig. 6.10(a) is expected. Regardless of the actual form of the transient, to my knowledge the data presented in Fig. 6.10(b) represent the first kinetic characterization of brittle microfracture events in any system under open-circuit corrosion conditions. The issue with regard to the form of the periodic oscillations must await detailed analysis of the system impedance. The kinetics of repassivation of brittle microfracture events is an issue of considerable theoretical importance in formulating models for crack propagation. The kinetics for the case shown in Fig. 6.10(b) yield a first-order rate constant of 0.029 s1. The value of the rate constant is found to depend on the

254

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

4

(a)

Current (μA)

2 0 –2 –4 –6

–8 43.0

43.5

44.0

45.0

44.5

45.5

Time (min)

(b) 2.5 2.0

Ln (I/I0)

1.5 1.0

0.5

0.0

–0.5 0.0

k = 0.029 s–1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Time (min)

Figure 6.10 Coupling current transient (a) and first order kinetic plot (b) of the microfracture event repassivation for fracture in AISI 4340 steel in 6 M NaOH at 70
C [13]. The rate constant for repassivation was found to depend upon the rolling direction of the steel plate from which the C(T) specimens were machined. The negative going current indicated in Fig. 6.10(a) indicates enhanced anodic dissolution at the crack tip [17].

The electrochemical nature of stress corrosion cracking

255

rolling direction of the steel ingot, from which the C(T) specimens were machined (as noted above), indicating an interesting material/electrochemistry coupling that, to my knowledge, has never previously been described. Using the expression, r ¼ ðD=f Þ1=2 , the microfracture dimension for cracking in AISI 4340 high SS may also be estimated. Although the diffusivity reported in the literature for hydrogen in carbon and low-alloy steels is highly scattered, a value of 1  107 cm2/s is selected from the review by Oriani [30]. The microfracture frequency was measured by Liu and Macdonald [17] as 0.003 s1. These data yield r ¼ 58 mm, which again is in satisfactory agreement with that obtained from the noise in the coupling current (r ¼ 49 mm) [16]. The conclusion that must be drawn is that the CGR is determined by two factors: (1) the microfracture frequency (f) and (2) the microfracture dimension (c). In a one-dimensional model it is evident that CGR ¼ Gfc2, in which the value of f is determined by the mechanics of the crack tip, with f ¼ ε_ =εf , where ε_ is the crack tip strain rate, εf is the fracture strain, and G ¼ 2/B. This issue is expanded below.

6.4

The coupled environment fracture model

Beginning in the early 1990s, Macdonald and Urquidi-Macdonald [6] began developing the CEFM in response to a review that they performed for a regulatory agency in Sweden. The review showed that none of the models then available for estimating CGR were deterministic; that is, the predictions were not explicitly constrained by the natural laws (eg, the conservation of charge), as all physicochemical systems must. Furthermore, many of the models were found to be either empirical correlations, with some being sophisticated, or purely mechanical in nature, even though it was well known that the CGR was a sensitive function of environmental parameters such as ECP and conductivity. Accordingly, it was evident that a new approach was called for if a robust, deterministic model was to be developed for predicting CGR in the alloys used in water-cooled nuclear reactor coolant circuits. Thus, in response to this need, Macdonald and Urquidi-Macdonald developed such a model in the form of the initial version of the CEFM. Since that time, the CEFM has undergone many iterations, each of which was made to address specific shortcomings of the model or in response to new experimental findings. It is not a goal of this chapter to present a detailed account of the CEFM, as that has been done elsewhere [2,6e10]. Instead, only a brief outline is given to identify key assumptions and constraints so that the reader may appreciate the physical basis of the model without having to wade through extensive mathematical detail. As noted above, the CEFM is based on the DAH, which is shown schematically in Fig. 6.1. The DAH, which was first postulated by Evans [1] in 1923, and which has long been accepted as being the theoretical basis for all forms of localized corrosion, postulates that, for geometric reasons, if the local anode and the local cathode become spatially separated, then localized corrosion will occur. If differential aeration is established, then a positive current must flow from the crack to the external surfaces, where

256

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

it is annihilated with the electron current flowing from the crack tip, as indicated in Fig. 6.3. The conservation of charge requires that Eq. [6.3] be satisfied: Z idS ¼ 0

[6.3]

S

where i is the net current density (partial anodic current density minus the partial cathodic current density) on the surface of area increment dS. The integral is carried out over the entire surface, including that in the crack and that on the external surface away from the crack mouth. On the external surface, the integral is evaluated at a sufficiently large distance from the crack mouth that the potential in the solution with respect to the metal is imperceptibly different from the negative of the corrosion potential (commonly less than 100 CODs (crack opening displacements) from the crack center line) or, equivalently, where i / 0. This distance depends on the solution conductivity, ECP, temperature, and the kinetics of the depolarizer reaction of the external surface (eg, the reduction of oxygen). With reference to Fig. 6.3, it is apparent that there exist two coupled mathematical problems that must be solved in describing crack growth, and that these problems are coupled by common boundary conditions (potential and specie concentrations) at the crack mouth. The mathematical equations than must be solved are the NernstePlanck flux and continuity equations (one for each species) and Poisson’s equation for the potential, subject to the electroneutrality condition. If we consider the problems separately, then an infinite number of solutions are obtained for each of the crack internal environment and external environments, depending on the value chosen for the potential at the crack mouth (4mouth). There is, however, only one potential at the crack mouth at which Eq. [6.3] holds. The way in which the electrostatic potential in the solution at the crack mouth is practically chosen is shown in Fig. 6.11. Briefly, in the numerical version of the CEFM [2e5] (an analytical version also exists [10]), two nestled iterations are performed. The first is on the equivalency of the current in the crack internal environment (originating mostly, but not totally, from the crack tip) and the current consumed on the external surfaces (Fig. 6.11(a)). These currents depend on the potential in the solution at the crack mouth (4mouth), and this is the parameter upon which the primary iteration is performed. However, during each primary iteration, it is necessary to determine the potential at the crack tip (4tip); this is accomplished by a secondary iteration on the electroneutrality condition at the crack tip, with the iteration being performed as indicated in Fig. 6.11(b). Thus, within each of the primary iterations, the secondary iteration is carried out on the crack tip potential. The iterations are continued until convergence is achieved, and the crack tip current is calculated using Tafel’s equation. This current is then converted into a crack growth rate via Faraday’s law. Once the crack mouth and the crack tip potentials are known, it is possible to calculate the polarization (IR potential drops) in the crack and in the external environments; typical modeling results are shown in Fig. 6.12. Thus, it is seen that as the temperature increases, the polarization for a given crack length in the internal environment increases while the polarization in the external environment decreases, until it appears to be negligible at a BWR operating temperature of 288
C. However, it is a mistake to conclude that the external polarization is unimportant and hence that it is possible

The electrochemical nature of stress corrosion cracking

(a)

(b)

CGR

Emouth

Internal current

Etip

Internal current

External current

Iint = Iect?

257

No

Crack tip current

Concentration profile in crack

Yes Electrochemical crack advance

Crack tip electroneutrality satisfied?

No

Yes End

End

Figure 6.11 Flow diagrams showing the iterations within the coupled environment fracture model on the conservation of charge (a) and crack tip potential (b). Note that iteration (b) occurs within each iteration (a) until convergence with the crack internal and external currents is achieved. CGR, crack growth rate. M. Vankeerberghen, D.D. Macdonald, Calculating the Temperature-Maximum and the Lower Potential Limit for the Crack Growth Rate in Type 304 SS Using the CEFM, CORROSION2003, Paper No. 03520, NACE International, Houston, TX, 2003.

to simply specify the potential (ECP) at the crack mouth. This approach is illegitimate because a sufficiently large gradient must exist to account for the flow of the coupling current from the crack to the external surfaces, as required by the conservation of charge, and because of the experimental demonstration [11,25] of the importance of the kinetics of the redox reactions on the external surface in determining the CGR. Accordingly, the condition, 4mouth > ECP must hold, however small the difference might be. Also, the calculations displayed in Fig. 6.12 correspond to a much higher conductivity (dilute sulfuric acid) than in the case of BWR primary coolant. In the latter case, the IR potential drop that is predicted in the external environment is considerably larger than displayed in the figure. Various crack tip strain rate models have been used in successive generations of the CEFM, and they are summarized in Table 6.1. Indeed, the current code allows selection of the crack tip strain rate model as a user input. The model by Ford et al. [20] is purely empirical and contains little theoretical justification; it does, however, yield an acceptable result. This can be shown by substituting KI ¼ 30 MPa Om, which yields a crack tip strain rate of 3.33  105 s1. Assuming the fracture strain to be 8  104, a microfracture frequency of 0.04 Hz is obtained. This value is significantly lower than the experimentally observed value of 2 Hz (Fig. 6.7), but given the uncertainty in the

258

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors 0.3

6.4 ECP Emouth Etip pH

0.2

External polarization 0

6.2 6.1

–0.1

6 Internal polarization

–0.2

5.9

–0.3

5.8

–0.4

5.7

–0.5

5.6

–0.6 0

50

100

150

200

250

300

pH (-)

Electrochemical pot. (V)

0.1

6.3

5.5 350

Temperature (°C)

Figure 6.12 The effect of temperature on the pH of the external environment, the electrochemical potential at the crack tip (Etip ¼ 4tip), the potential at the crack mouth (Emouth ¼ 4mouth), and on the potential in the external environment (electrochemical corrosion potential (ECP)) during crack growth in type 304 stainless steel in dilute sulfuric acid solution with an ambient temperature (25
C) conductivity of 0.27 mS/cm and a dissolved oxygen concentration of 200 ppb. The data were calculated using the coupled environment fracture model after calibration at 288
C and assuming a crack tip strain rate thermal activation energy of 100 kJ/mol (Congleton crack tip strain rate model). Note that the potentials 4tip and 4mouth are electrostatic potentials in the solution with respect to the metal, whereas Etip, Emouth, and ECP are potentials of the metal with respect to a reference electrode, in this case the standard hydrogen electrode. M. Vankeerberghen, D.D. Macdonald, Corros. Sci. 44 (2002) 1425e1441.

fracture strain, it is difficult to quantify how serious this difference might be. The Congleton expression [31] for the crack tip strain rate is based on linear elastic fracture mechanics and hence has a good theoretical basis, especially for brittle solids. The expression by Shoji et al. [32] is also well-based within fracture mechanics theory and allows for strain hardening. Most of the calculations reported in this chapter have been performed using the expressions for the crack tip strain rate by either Congleton et al. [31] or Shoj et al. [32]. Note that in both of these expressions the crack tip strain rate depends on the CGR, and therefore the expressions are transcendental. Accordingly, the crack tip strain rate must be solved for iteratively, which adds significantly to the execution time of the code (Fig. 6.13). In the remainder of this chapter, theoretically predicted CGRs as a function of various independent variables are presented to illustrate predictions using the CEFM and to resolve some long-standing issues in the science of SCC. These calculations use the default conditions summarized in Table 6.2, unless otherwise noted. The default model parameter values are summarized in Table 6.3. An important issue that must be addressed is why the microscopic fracture events occur at all. Although much has to be done to resolve specific details of fracture

Crack tip strain rate

Equations

Definitions

Ford

ε_ ct ¼ 4:11  1011 K 4
    2 sy Rp ÞK 2 ε_ ct ¼ ar_ 63:653pa ð1n þ b sy E E ln r

Crack tip strain rate (s1) sy: Yield strength (MPa) E: Elastic (Young’s) modulus (MPa) _ Crack growth rate (m/s) a: K: Stress intensity factor (MPa Om) Rp: Plastic zone size (m) r: The distance from a growing crack tip (m) nGH: Strain-hardening exponent by Gao and Hwang a, b, b1, l: Dimensionless constants in plastic strain calculation Q: Thermal activation energy (J/mol) R: Gas constant (J/mol$K) T: Temperature (K)

Congleton

 

s b1 Ey


  2  1 nGH 1 K ln lr ½ar_ sy

Shoji

ε_ ct ¼

Temperature effect


 ε_ ct ðTÞ ¼ ε_ ct ð288
CÞexp QR T1  288 þ1273:15

nGH nGH 1

The electrochemical nature of stress corrosion cracking

Expressions for crack tip strain rate for different models developed for estimating crack growth rate in sensitized type 304 stainless steel

Table 6.1

259

260

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

(a) t

1st

2nd

3rd

c

(b) t

(c) t

1st

2nd

3rd

1st

2nd

c

(d) t

3rd

k c

Figure 6.13 Creep model by Vitek and Wilkinson [33] illustrating the nucleation of voids ahead of the crack tip as the crack grows from (a) to (d) and the periodic rupture of the intervoid ligaments. c ¼ intervoid spacing.

Default system parameters used in coupled environment fracture modeling of crack growth rate in sensitized type 304 stainless steel in boiling water reactor primary coolant circuits [34]

Table 6.2

Parameter

Value

Temperature

288
C

Crack opening

0.001 cm

Crack width

1.0 cm

Pipe hydrodynamic diameter

50 cm

Flow velocity

100 cm/s

Stress intensity factor

27.5 MPa Om

O2 concentration

100 ppb

H2 concentration

1 ppb

H2O2 concentration

1 ppb

The electrochemical nature of stress corrosion cracking

261

Default values of parameters in the coupled environment fracture model for modeling crack growth in type 304 stainless steel in boiling water reactor primary coolant (pure water at 2888C) [34]

Table 6.3

Parameter

Value

Atomic volume (m3)

1.18  1029

Fracture strain of oxide film, εf

8  104

Young’s modulus, E (MPa)

2  105

Dimensionless constant, b

5.08

Density, r(g/cm )

8

Yield strength, sy (MPa)

215

Strain hardening exponent, n

1.7

Dimensionless constant, l

0.11

Shear modulus, G (Pa)

7.31  1010

Grain boundary self-diffusion coefficient, Db0 (m2/s)

2.50  104

Activation energy for diffusion, (kJ/mol)

168

Grain-boundary diffusion width (m)

5  1010

Tafel slope for HER

0.065

i0 for HER, (A/cm2)

5  104

Tafel slope for ORR

0.071

3

I0 for ORR, (A/cm )

5.05  103

Passive current density at steady state, (A/cm2)

2.6  103

Standard electrochemical potential for stainless steel dissolution reaction, E0 (Vshe)

0.47

2

mechanisms in SSs in high-temperature aqueous solutions (eg, Ref. [34]), the observations of this work are best explained by a brittle microfracture mechanism in which the events are induced by hydrogen [21e24] or possibly by dealloying [27,28], as noted above. Thus, it is postulated that the mean current exiting the crack mouth, which is detected by the ZRA, generates a sufficiently acidic environment at the crack tip that hydrogen evolution occurs and atomic hydrogen is injected into the matrix of the Cr-depleted grain boundary ahead of the crack, which may have become susceptible to HIC via the formation of strain-induced martensite [24] (see below). Subsequently (and periodically), a fracture event initiates in the matrix in front of the crack tip, at which the hydrostatic stress and the hydrogen concentration, in concert, exceed critical conditions. This “martensite/hydrogen-induced fracture” mechanism

262

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

is postulated in spite of the fact that the environment external to the crack (but not that at the crack tip) is under oxidizing conditions. Recent modeling studies that have taken into account coupling between the crack internal and external environments indicate that increasing the oxidizing power of the external environment (eg, by increasing the concentration of oxygen and hence the ECP) lowers the crack tip pH and hence enhances the rate of hydrogen evolution at the crack tip [6e10,34]. This change favors the injection of hydrogen into the matrix ahead of the crack tip. A similar (“void nucleation/hydrogen pressurization”) mechanism can be formulated by combining the hydrogen injection/recombination hypothesis with void nucleation at an appropriate microstructural feature ahead of the crack tip (eg, at grain boundary precipitates) [22,23,33]. Recombination of atomic hydrogen in the void creates a hydrogen pressure that contributes to the local hydrostatic stress. As the internal void pressure builds, a local stress is reached at which brittle fracture occurs forward and backward, with the latter linking up with the main crack. This mechanism should result in an increase in the brittle microfracture event frequency with increasing stress intensity at low stress intensities (Fig. 6.9), but at higher stress intensities the pressurization of the void is expected to be of paramount importance, and hence the frequency might be expected to become only weakly dependent on stress intensity, as observed. The impact of differential aeration and hence coupling between the internal and external crack environments has been explored theoretically; the results are displayed in Figs. 6.14 and 6.15. Fig. 6.14 shows that Naþ is rejected from the crack, whereas Cl is concentrated within the cavity, as the intensity of differential aeration (reflected by the oxygen concentration and hence by the ECP) increases. In both cases the concentrating factor is predicted to be about 106 and 106, respectively. Electroneutrality within the crack is maintained by replacing Naþ with Hþ produced by the

10

0.1 μS/cm 0.5 μS/cm

10–8

10–10

10–12

10–14

–0.8

–0.6

–0.4

–0.2

0.0

0.2

Electrochemical potential, ECP (Vshe)

Cl– concentration at crack tip (mol/L)

Na+ concentration at crack tip (mol/L)

102 Solution conductivity

–6

0.4

Solution conductivity 10

0.1 μS/cm 0.5 μS/cm

0

10–2

10–4

10–6

–0.8

–0.6

–0.4

–0.2

0.0

0.2

0.4

Electrochemical potential, ECP (Vshe)

Figure 6.14 Calculated [Naþ] and [Cl] concentrations at the crack tip as a function of electrochemical corrosion potential for type 304 stainless steel in 288
C water for different values of ambient temperature conductivity [35]. The parameter values used in the predicted concentrations can be found in Table 6.3.

The electrochemical nature of stress corrosion cracking

263

7 Solution conductivity 0.1 μS/cm 0.5 μS/cm

6

pH at crack tip

5 4 3 2 1 0 –0.8

–0.6

–0.4

–0.2

0.0

0.2

0.4

Electrochemical potential, ECP (Vshe)

Figure 6.15 Plot of crack tip pH versus electrochemical corrosion potential for two different conductivity values. The parameter values used are listed in Table 6.3 [35].

hydrolysis of metal cations (Fe2þ, Cr3þ, and Ni2þ) and by the hydrolyzed cations themselves (eg, Fe(OH)þ, Cr(OH)2þ, and Ni(OH)2þ), resulting in the pH versus ECP predictions summarized in Fig. 6.15. If the pH is not too low, solid oxides such as Fe3O4, Cr2O3, NiO, NiFe2O4, FeCr2O4, NiCr2O4, and so forth may be precipitated in the crack, as was observed by Thomas and Bruemmer [36]. Thus, the calculations displayed in Fig. 6.15 are in concert with the expectation of significant crack acidification, which is the direct result of differential aeration. As postulated elsewhere in this chapter, the crack tip is in a quasi-depassivated state because of the very low pH and the high chloride concentration at the crack tip. This state results in hydrogen evolution that consumes some of the coupling current that is released by dissolution of the metal at the crack tip. Some of this hydrogen enters the matrix, resulting in embrittlement of the matrix, possibly because of the presence of strain-induced martensite [24]. Thus the crack grows by strain-induced, periodic fracture of the matrix ahead of the crack tip, as shown by the noise in the coupling current (Fig. 6.5). The frequency with which microfracture events occur (f) is determined by the crack tip strain rate and the fracture strain. The distance ahead of the crack that fractures (c) because of embrittlement is known as the fracture dimension, and the CGR in a one-dimensional model is simply given by CGR ¼ Gfc2, where G ¼ 2/B. The calculated fracture frequency and the microstructure dimension are plotted in Fig. 6.16(a) and (b), respectively. The two fracture mechanicsebased models (Congleton et al. [31] and Shoji et al. [32]) predict that the microfracture frequency increases sharply with increasing CGR, as expected from the dependence of fracture frequency on KI (Fig. 6.6) and from the dependence of the relationship, CGR ¼ Gfc, provided that c

264

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

(b)

10–1 KI = 27.5 MPa √m

101

10–2

10–1

Flow velocity = 100 cm/s Temp = 288°C Solution conductivity: 0.1 μS/cm

10–3

10–3 Congleton Shoji Ford

10–5 10–7 10–10

Microfracture dimension, r (cm)

Microfracture frequency, f (Hz)

(a)

Solution conductivity: 0.1 μS/cm 10–9

10–8

10–7

Crack growth rate, CGR (cm/s)

10–4

10–5 10–10

10–9

10–8

10–7

Crack growth rate, CGR (cm/s)

Figure 6.16 Calculated microfracture event frequency (a) and microfracture dimension (b) based on different models for calculating the crack tip strain rate and the calculated crack growth rate for intergranular stress corrosion cracking in type 304 stainless steel in water at 288
C [35].

is only weakly dependent on stress intensity and hence on CGR. Because c is expected to be determined by the diffusion length of hydrogen in the matrix ahead of the crack, or by the spacing of Cr carbide (C23C6) precipitates on the grain boundaries, it is evident that it should not depend on KI or on any environmental variable. As shown in Fig. 6.16(b), the microfracture dimension at low CGR values decreases sharply in the mechanical fracture region, but in the SCC region (CGR > 4  109 cm/s) the microfracture dimension is predicted to be almost independent of CGR. By assuming that the crack tip strain rate is thermally activated and follows an Arrhenius-type temperature dependence, the temperature dependence of the CGR can be estimated and compared with experimental data. The comparison is shown in Fig. 6.17 for the three models used in the CEFM for calculating the crack tip strain rate (Table 6.1). All three expressions provide a reasonable account of the experimental data [37], but it is evident that the scatter in the data is such that no distinction between the strain rate models can be made. Returning now to the noise structure of the coupling current, it is noted that if conditions exist under which the microfracture events are not delineated in the time domain, the noise in the coupling current appears as “unstructured noise” arising from many microfracture events occurring more or less simultaneously across the crack front. An important question is then, “Can any useful information be extracted from that noise?” The components of the noise, together with the frequencies at which they occur, can be determined by a number of time-to-frequency transformation algorithms, namely, (1) fast Fourier transformation (FFT), (2) the maximum entropy method, and (3) wavelet analysis (WA). In my and my colleagues’ previous work on SCC in sensitized type 304 SS in thiosulfate solution at 22
C [17,18], we used

The electrochemical nature of stress corrosion cracking

265

Crack growth rate, CGR (cm/s)

10–6 Cogleton Ford Shoji Experimental data

(O2) = 200 ppb

KI = 33 MPa √m S = 9.62 ppb

10–7

10–8

0

50

100

150

200

250

300

350

Temperature, T (°C)

Figure 6.17 The effect of temperature on crack growth rate in type 304 stainless steel in dilute sulfuric acid solution with an ambient temperature (25
C), a conductivity of 0.27 mS/cm, and a dissolved oxygen concentration of 200 ppb [15]. Experimental data are from Andresen [37]. Solid lines are predictions of the coupled environment fracture model using various crack tip strain rate models for estimating the crack tip strain rate.

both FFT and WA to extract frequency-domain information from the time-domain coupling current record. Typical amplitude spectral density plots constructed by FFT on the coupling current noise for IGSCC in sensitized type 304 SS in 0.5 M thiosulfate solution at 22
C as a function of sensitization time [18] are shown in Fig. 6.18. It is evident from examining the time-domain record (Fig. 6.19) that, although the noise is pseudo-random, a certain underlying periodicity is indicated with a frequency range of 10e50 h1 (2.8e13.9  103 Hz), not counting those within the short periods of intense activity, corresponding to the low-frequency end of the amplitude spectral density plot (Fig. 6.18). Indeed, we subsequently identified the lowfrequency noise as arising from hydrogen-assisted IGSCC. Noise at frequencies greater than 0.1 Hz is considered to be extraneous because it is present at the same amplitude in the absence of a load. WA was performed on the coupling current data from the fracture of sensitized type 304 SS in thiosulfate solution, and typical energy plots are shown in Fig. 6.20 for successive loading cycles. These graphs plot the fraction of the total signal (noise) energy contained within a preselected frequency range (ie, within a “bin” or a “crystal”), as a function of frequency. Thus, with reference to Fig. 6.20, it is evident that a maximum in the fraction of energy contained in each bin occurs within the frequency ranges covered by crystals D5 to D11, which covers the frequency range from 0.977 to 125  103 Hz (Table 6.4). This range is somewhat wider than that determined directly from the coupling current record, and is much lower than the microfracture frequency that is observed in IGSCC in sensitized type 304 SS in high-temperature

266

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

1e–4 1e–5

Amplitude (A)

1e–6 1e–7 1e–8 1e–9 1e–10

4h sensitized 14h sensitized 24h sensitized

1e–11 0.0001

0.001

0.01

0.1

1

Frequency (Hz)

Figure 6.18 Amplitude spectral density plots for intergranular stress corrosion cracking in sensitized type 304 stainless steel in 0.5 M thiosulfate solution at 22
C as a function of sensitization time [18]. M. Gomez-Duran, D.D. Macdonald, Corros. Sci. 48 (2006) 1608.

water (2 Hz; Fig. 6.9). Importantly, upon correcting for temperature using an Arrhenius-type temperature dependence for the crack tip strain rate with an activation energy of 40 kJ/mol [9], it is estimated that the microfracture frequency should be 1.04  103 Hz at ambient temperature, which is in satisfactory agreement with the values given above. Thus it is concluded that the oscillations in the coupling current from IGSCC in sensitized type 304 SS in high-temperature water and in thiosulfate solution at 22
C have the same origin ðf ¼ ε_ =εÞ. However, it is also apparent that WA detects noise other than that which arises from microfracture at the crack tip. This is confirmed by the fact that the greatest energy content is found for the unloaded condition and that the energy content decreases systematically with successive loadings, corresponding to the lengthening of the crack [18,19]. As postulated by Gomez-Duran and Macdonald [18,19], the source of the extraneous noise is probably intergranular attack via dissolution of the steel at emergent Cr-depleted grain boundaries or possibly hydrogen evolution at the same location. Nevertheless, the range (2.8e13.9  103 Hz) is determined by the direct examination of the time record of the coupling current (Fig. 6.19). As noted above, WA analysis of the coupling current noise, and the direct examination of the noise itself, for IGSCC in sensitized type 304 SS in thiosulfate-containing solutions reveals microfracture events that occur over a wide range of frequencies. Examination of the time record (eg, Fig. 6.19) allows an estimation of the frequency of events that result in pulsations in the coupling current because of the partial

35

1.4

30

1.2 1

20 0.8 15 0.6 10

Loading (k|bf)

Current (μA)

25

The electrochemical nature of stress corrosion cracking

24 h sensitized 304 SS in 0.5 M thiosulfate solution

0.4 5 0.2

0 0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4 0

–5 Time (h)

Figure 6.19 Coupling current and load versus time for intergranular hydrogen-induced cracking in sensitized type 304 stainless steel (SS) (24 h at 650
C) in 0.5 M Na2S2O3 at 22
C for a stress intensity factor (KI) of 21.5 MPa Om [18,19]. Note the residual periodicity in the coupling current, which is reminiscent of that shown in Fig. 6.8, suggesting that the conditions chosen for the experiment were not too different from those that would have resulted in clear delineation.

267

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

D17

D16

D15

D14

D13

D12

D11

D10

D9

D8

D7

D6

D5

Before load First load Second load Third load Fourth load

D4

0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

D3

Fraction of total energy (%)

268

Crystal

Figure 6.20 Wavelet analysis of the noise in the coupling current from sensitized type 304 stainless steel (4 h at 650
C) in 0.5 M Na2S2O3 at 22
C, with a stress intensity factor (KI) of 21.5 MPa Om. [19]. The maxima in the fractional energy are the result of localized corrosion (intergranular attack), not to intergranular stress corrosion cracking.

Frequency of crystals in the wavelet analysis of intergranular stress corrosion cracking in sensitized type 304 stainless steel in thiosulfate-containing solution at 228C [19]

Table 6.4

Crystal

Minimum frequency (mHz)

Maximum frequency (mHz)

D3

250,000

500,000

D4

125,000

250,000

D5

62,500

125,000

D6

31,250

62,500

D7

15,625

31,250

D8

7813

15,625

D9

3906

7813

D10

1953

3906

D11

977

1953

D12

488

977

D13

244

488

D14

122

244

D15

61

122

D16

30.5

61

D17

15.3

30.5

The electrochemical nature of stress corrosion cracking

269

delineation of the events in the time domain. The principal components occur over the frequency range of 2.8e13.9  103 Hz, with an average value of 8.35  103 Hz (Figure 6.20, Table 6.4). Combined with CGR data (3  105 cm/s [18,19]), this frequency corresponds to a microfracture event size of about 478 mm), which is significantly larger than the 60 mm originally estimated using a higher microfracture frequency [18,19], indicating that the microfracture event may extend over multiple grains. Because a distribution exists, it was estimated that some microfracture events may have sizes over a considerable range (370e825 mm), but this estimate is highly dependent on the microfracture events being semicircular and on the CGR for each grain being the same as the average CGRdassumptions that are probably not entirely valid but are made here because the exact geometry of the event and the local CGR cannot be determined. In any event, the microfracture dimension is such that the classical SDR model [20] can be ruled out. In this regard, it must be noted that IGSCC of sensitized type 304 SS in thiosulfate-containing solutions is regarded as being a classic case of hydrogen embrittlement. Thus, the CEFM is consistent with a mechanism that postulates that crack growth occurs by a synergistic combination of brittle fracture and HIC events, which are postulated to occur simultaneously at the crack tip. Thus differential aeration maintains the crack tip in a semi-depassivated state, such that hydrogen in injected into the matrix, which probably contains significant amounts of strain-induced martensite, resulting in HIC over the microfracture dimension when the combined crack tip strain and the properties of the embrittled matrix exceed a critical value. Crack growth, which is envisioned to occur via a continuous stream of microfracture events, is defined by two parameters: the microfracture frequency (f) and the microfracture dimension (c), such that da/dt ¼ Gfc2, as previously noted. The value of f is determined primarily by the crack tip strain rate in response to the applied load and by the fracture strain, _ whereas the fracture dimension is determined by the length of the zone ahead f ¼ ε/ε, of the crack tip that becomes embrittled by hydrogen and also by the precipitate spacing on the grain boundaries. Regardless of the exact details, this microfracture mechanism seems to account for all of the available data, with f accounting for the dependence of the CGR on KI and c accounting for the magnitude of the CGR. Finally, it is important to note that the proposed mechanism differs in one important respect from the classical SDR mechanism proposed by Ford et al. [20]. In the SDR mechanism, the entity at the crack tip that is envisioned to fracture is the oxide film, followed by (or perhaps simultaneously with) slip with a dimension that is limited to a few multiples of the Burgers vector for the slip system (ie, fractions of a nanometer), whereas in the mechanism proposed here it is the hydrogen-embrittled matrix ahead of the crack tip that fractures over a dimension that is determined by the diffusion length of hydrogen, or perhaps by the spacing of carbides on the grain boundary (micrometer dimensions).

6.5

The role of the electrochemical crack length in SCC

Earlier in this chapter it was argued that SCC can only be described accurately by defining two crack lengths: the mechanical crack length (MCL), which along with the applied mechanical load defines the mechanical state of the crack tip in terms of

270

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

the stress intensity factor, KI, and the ECL, which partially determines the coupling current and its dependencies on the typical electrochemical independent variables (potential, conductivity, etc.). Physically, the ECL is the length of the path of least (electrical) resistance between the crack front and the external surface, where the coupling current is annihilated via a charge transfer reaction, such as oxygen reduction, whereas the MCL is the distance between the crack front and the mechanical load line. The difference between the MCL and the ECL may be appreciated by considering a classical C(T) fracture mechanics specimen. Thus the MCL increases as the crack grows, whereas the ECL, which corresponds to the least-resistant path to the specimen side surfaces, remains essentially constant. Little has been reported in the literature on experimentally defining the importance of the ECL, so most of the discussion in this section is based on theoretical prediction using the CEFM [2e6]. Fig. 6.21 plots the calculated CGR in sensitized type 304 SS as a function of potential (ECP) for crack lengths ranging from 0.001 to 10 cm. It is predicted that, for any given corrosion potential where environmental effects dominate (ie, for ECP > Ecrit), the CGR decreases with increasing ECL (L) or, equivalently, that a higher ECP must be applied to yield the same CGR as the ECL increases. This latter finding is equivalent to stating that the critical ECP for the onset of environmentally influenced fracture, Ecrit, becomes more positive as the ECL increases. This latter conclusion has very important practical implications. One can imagine a situation where the ECP may have a value of 0.05 Vshe, which is more positive than the critical potential for a short crack. As the crack grows, the critical potential becomes more positive, such that the

Crack growth rate, CGR (cm/s)

10–6

10–7

Crack length (cm) 0.001 0.01 0.1 1 10

10–8

10–9

10–10 –0.6

–0.4

–0.2

0.0

0.2

Electrochemical potential, ECP (Vshe)

Figure 6.21 Dependence of crack growth rate calculated using the coupled environment fracture model on electrochemical corrosion potential for type 304 stainless steel in water at 288
C as a function of crack length [38]. The other parameters are as in Table 6.3.

The electrochemical nature of stress corrosion cracking

271

driving force for crack propagation, ECP  Ecrit, decreases. This causes the CGR to decrease and become zero at ECP ¼ Ecrit. At this point, the crack is electrochemically “dead” and will not propagate further unless ECP becomes more positive, although it will continue to propagate by creep. Thus the theory predicts that all cracks reach limiting depths; that is, eventually all stress corrosion cracks must “die.” The critical question, then, is, “Will the cracks die before they induce failure in the system?” While I am unaware of any experimental demonstration of this prediction in SCC, it has been demonstrated in the case of pitting corrosion, which is phenomenologically very similar to SCC in terms of electrochemistry [39]. The coupling current is also predicted to be a function of the corrosion potential, as shown in Fig. 6.22. As expected, the coupling current is expected to increase roughly exponentially with corrosion potential because of the close relationship between the coupling current and the CGR, as depicted in Fig. 6.6. As the ECL increases, the coupling current decreases because of the increasing IR potential drop down the crack that subtracts from the potential that is available to drive the reduction of oxygen on the external surface. Fig. 6.21 demonstrates theoretically that under conditions where IGSCC dominates CGR, a linear relationship between the coupling current and the CGR exists, as has been demonstrated experimentally (Fig. 6.4). Over a much more extended range of

Coupling current (A)

1e–5 1e–6

COD = 5 x 10–4 cm, Crack width = 1.0 cm, KI = 27 MPa √m, V = 100 cm/s, d = 50 cm, T = 288°C, (H2) = 10–4 ppb,

1e–7

(H2O2) = 10–4 ppb, (Na+) = 1.35 ppbNa,

1e–8

(H2SO4) = 10–6 ppbS, (O2) = 1–2.33 x 106 ppb, κ 288 = 2.69 μS/cm, κ 25 = 0.0618 μS/cm,

1e–9

Creep rate = 1.61x10–10 cm/s.

1e–10 1e–11

L = 0.1 cm L = 0.5 cm L = 1.0 cm L = 2.0 cm L = 5.0 cm L = 10 cm L = 20 cm L = 50 cm

1e–12 1e–13 1e–14 1e–15 1e–16 –0.8

–0.6

–0.4

–0.2

0.0

0.2

0.4

Corrosion potential (Vshe)

Figure 6.22 Predicted dependence of the coupling current (CC) on the corrosion potential for intergranular stress corrosion cracking in sensitized type 304 stainless steel under boiling water reactor primary coolant conditions as a function of the electrochemical crack length (ECL; L). The values for other parameters are listed in the figure. Note that, as the ECL increases, the CC decreases and eventually drops below the critical value of 1 nA. At that point the crack ceases to grow via the environmental mechanism and “dies” because differential aeration can no longer be sustained [15].

272

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

CGR for IGSCC in sensitized type 304 SS under BWR primary coolant conditions, as a function of the ECL (L), the relationship is no longer linear but can be deconvolved into two arms. The upper arm, corresponding to CGRs that are much higher than the creep rate, the relationship is as is shown in Figs. 6.4 and 6.23. At lower CGRs that are typical of creep, the relationship is a vertical one, indicating that the CGR is independent of the coupling current, as is expected for crevice corrosion in which the crack is inactive because the potential was more negative than Ecrit. Note that the coupling current versus CGR data all lie on a common locus, regardless of the crack length and regardless of whether fracture is mechanical (creep) or electrochemical in nature. The critical coupling current for the dominance of environmental effects in crack growth corresponds to that at the “knee,” or about 1 nA. Because of the independence of the CGR and coupling current on crack length in these plots, it is evident that a more accurate specification of critical conditions for the onset of IGSCC would be in terms of a critical coupling current. In this way the impact of ECL on Ecrit would be eliminated. Because the coupling current is easily measured using specimens of the type described by Manahan et al. [16], it is my opinion that this would be a practical way of monitoring for the existence of critical conditions for IGSCC in BWR coolant conditions. The practical impact of the dependence of the CGR on the ECL may be illustrated as follows. Consider the IGSCC of sensitized type 304 SS in the heat-affected zone of the H3 weld at the top of the core shroud of a BWR operating in Taiwan. Macdonald et al. [40] modeled crack growth in the shroud using technical information (coolant

1e–5 1e–6 1e–7

L = 0.1 cm L = 0.5 cm L = 1.0 cm L = 2.0 cm L = 5.0 cm L = 10 cm L = 20 cm L = 50 cm

Coupling current (A)

1e–8 1e–9 1e–10 1e–11

COD = 5 x 10–4 cm, Crack width = 1.0 cm, KI = 27 MPa √m, V = 100 cm/s, d = 50 cm, T = 288°C, (H2) = 10–4 ppb,

1e–12 1e–13

(H2O2) = 10–4 ppb, (Na+) = 1.35 ppbNa,

1e–14

(H2SO4) = 10–6 ppbS, (O2) = 1–2.33 x 106 ppb, κ 288 = 2.69 μS/cm, κ 25 = 0.0618 μS/cm,

1e–15 1e–16

Creep rate = 1.61x10–10 cm/s.

1e–10

1e–9

1e–8

1e–7

1e–6

Crack growth rate (cm/s)

Figure 6.23 Plot of calculated coupling current versus crack growth rate for intergranular stress corrosion cracking in sensitized type 304 stainless steel in boiling water reactor primary coolant (water at 288
C), showing the creep arm and the stress corrosion cracking arm [15].

The electrochemical nature of stress corrosion cracking

273

chemistry, operating history, etc.) supplied by the reactor operator or that was available in the open literature. The integrated damage (crack length vs time) was modeled using the ALERT code, which contains the CEFM to calculate the CGR at each state point defined by a given set of conditions, to predict the history of a crack in the shroud with an initial length of 0.5 cm. The results are shown in Fig. 6.24 for three operating scenarios differing in whether HWC had been enacted and when it was adopted over a 10-year (120-month) operating period. HWC involves the addition of small amounts of hydrogen (typically 0.5 ppm) to the feedwater of a BWR with the objective of displacing the ECP of the SS in the primary coolant system to a value that is below Ecrit (0.23 Vshe at 288
C) [41]. However, extensive modeling [40,42e44] has shown that HWC can only be partially successful because for many components in a BWR primary coolant circuit the ECP is not displaced below the critical potential. Note that the crack length is roughly parabolic because the CGR decreases with increasing crack length. If the CGR model had not recognized the dependence of CRG on ECL, the extent of damage (crack depth) would have been greatly overestimated, as can be seen by extrapolating the tangent to the crack depth versus time at t ¼ 0 to longer times, and would have predicted that an unacceptably long crack would have formed

3.5 Normal water chemistry

3.0

Hydrogen water chemistry Normal to hydrogen water chemistry

Crack depth (cm)

2.5 2.0 1.5 1.0 0.5 0.0 0

20

40

60

80

100

120

Time (months)

Figure 6.24 Predicted histories of a growing crack in the heat-affected zone of an H3 weld in the core shroud of an operating boiling water reactor as a function of preconceived future operating histories. Note that the discontinuities in the crack length arise from changes in crack growth rate during outages (irregular outages). Note also that hydrogen water chemistry (HWC) has a major impact on the accumulation of stress corrosion crack damage and that the effect is more pronounced the earlier that HWC is applied. The effect of HWC is to reduce the crack growth rate by displacing the electrochemical corrosion potential in the negative direction [40].

274

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

over the 10-year operating period. To my knowledge, the CEFM, which was used to calculate the CGR, is the only model for crack growth in metals and alloys that predicts a dependence of CGR on the ECL.

6.6

Semielliptical cracks

The dependence of the CGR on ECL provides a ready explanation for the shapes of cracks in C(T) specimens and in planes (ie, surface cracks). In the case of a C(T) specimen, the ECL is distributed, ranging from a short distance from the crack tip at the side surface to the much longer distance from the crack tip midway across the specimen to the exposed side surfaces upon which the cathodic reaction occurs. Accordingly, the stress corrosion CGR is higher at the regions of intersection of the crack with the side surfaces, leading to a convex crack front as observed from aft of the crack. On the other hand, if crack growth is purely mechanical in nature (eg, creep), the CGR at the intersection of the crack with an exterior surface is predicted and found to be less that that midway across the crack front because of plane stress versus plane strain considerations. This leads to a concave crack front, as observed from aft of the crack and as commonly observed in experiments. In the extreme of this case, the crack may grow along the side surface, as shown in Fig. 6.25, because of the presence of side groves. Because the ECL from the sides is small and hence the CGR is high, crack penetration occurs from the side grooves rather than at the main crack front. The result is the formation of a “remaining ligament,” as shown in the micrograph presented in Fig. 6.25. The same principles account for the formation of elliptical surface cracks of the type that are frequently observed in BWR piping and other components [38]. Thus, the smallest ECL exists at the two points of intersection of the initial semicircular crack nucleus with the surface, whereas the largest is midway along the crack front. Accordingly, the CGR is fastest at the former and slowest at the latter, leading to the progressive development of a semielliptical crack with its major axis along the surface. From the work of Wang and Lambert [45,46], it is evident that, for a uniformly loaded surface crack in a finite thickness plane, the stress intensity factor is highest midway along the crack front (ie, at the point of intersection of the minor axis with the crack front) and is lowest at the points of intersection of the crack edges with the surface. This should result in the development of an elliptical crack with its major axis perpendicular to the surface. To my knowledge, this orientation is never observed; semielliptical cracks appear always to be oriented with the major axis coincident with the steel surface. The development of a theory for the growth of semielliptical cracks begins with recognizing that the CGR depends on the ECL, as illustrated in Fig. 6.18 [38]. Next, the equation of an ellipse (Fig. 6.26) is written as 

2   y þ ¼1 Lmajor Lminor x

[6.4]

The electrochemical nature of stress corrosion cracking

275

Crack propagation

Side grooves

Fatigue crack

Intergranular crack

Mechanical fracture

Figure 6.25 Scanning electron micrograph (top) of the fracture surface of a sensitized type 304 C(T) specimen after crack propagation in 15 ppm NaCl þ 150 ppb O2 at 250
C under continuous stirring conditions. Crack propagation from the side surfaces is apparent [15]. y

Lmajor

x

Lminor

Figure 6.26 Geometrical form of an ellipse. A semiellipse is the form below or above the major axis.

276

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

where Lmajor and Lminor are the major and minor axes, respectively. The CGR is then estimated along these axes using the recursive formulae   dL Lmajor ðj þ 1Þ ¼ Lmajor ð jÞþ dt L¼L0

[6.5]

and  Lminor ðj þ 1Þ ¼ Lminor ð jÞþ

dL dt

 [6.6] L¼LðjÞ

In these expressions, ðdL=dtÞL¼L0 and ðdL=dtÞL¼LðjÞ are the CGRs along the major axis at the intersection of the crack with the surface and along the minor axis at the midpoint along the crack front, respectively, as shown in Fig. 6.27. Note that the CGR at the intersection of the crack with the surface is a constant because the ECL is constant, but the CGR at the crack tip on the minor axis is that for an ECL corresponding to the length of that axis, and hence must be updated upon each iteration of j. Because the CGR is a function of the mode I stress intensity factor (KI), which in turn is a function of the MCL and the angular position along the crack front, as illustrated in Fig. 6.25, the stress intensity factor is a function of the position along the crack front. The stress intensity factor, as reported by Lee and Kim [47], is given by KI ¼

pffiffiffiffiffiffi   1=4 so pa 2 a b sin q þ a2 cos2 q f a; ; ; q B W EðkÞ

[6.7]

z x

2L 2b

2W

a

a y

B

Figure 6.27 Semielliptical surface crack in a plate [38,47].

2b

The electrochemical nature of stress corrosion cracking

277

Eq. [6.7] readily shows that the stress intensity factor values for the two axes are related: rffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffi  Lmajor p b KI q ¼ [6.8] ¼ KI ðq ¼ 0Þ  0:909 ¼ 0:909KI ðq ¼ 0Þ 2 a Lminor   Thus it is evident that when b/a < 1.21, then KI q ¼ p2 > KI ðq ¼ 0Þ, and the crack should propagate more rapidly perpendicular to the surface rather than at the intersection of the crack with the surface plane, as noted above. Typical predictions of the CGR perpendicular to the surface (Lminor) and along the surface (Lmajor) with respect to elapsed time for type 304 SS in a BWR environment at 288
C are displayed in Fig. 6.28. The plots show that the CGR perpendicular to the surface (minor axis) monotonically decreases with time, whereas the CGR along the surface (major axis) remains constant. However, the predicted stress intensity factor (KI) at the crack center (ie, at the tip of the minor axis) increases with elapsed time, as shown in Fig. 6.29. Thus, if the normal relationship between CGR and KI were to hold, the CGR at the crack center should increase with time. Clearly, the impact of increasing the ECL, leading to a decrease in CGR, outweighs the impact of increasing the stress intensity factor, which should give rise to an increase in CGR, resulting in the CGR decreasing with elapsed time. Integration of the CGR along

Crack growth direction

Lmajor Lmajor

Crack growth rate, CGR (cm/s)

10–7

Lmajor w/o increase in KI

10–8

Conductivity: 0.11 μS/cm KI: 25.0 MPa √m 10

–9

Flow velocity: 100 cm/s (O2): 100 ppb T: 288ºC 0

200

400

600

800

1000

Time, t / h

Figure 6.28 Predicted crack growth rates perpendicular to the surface (Lminor) and along the surface (Lmajor) with respect to elapsed time for type 304 stainless steel in a boiling water reactor environment at 288
C [38].

278

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

100

Stress intensity factor, SIF (MPa √m)

Conductivity: 0.11 μS/cm KI: 25.0 MPa √m

80

Flow velocity: 100 cm/s (O ): 100 ppb 2

T: 288ºC

60

40

20

0

200

400 600 Time, t / h

800

1000

Figure 6.29 Predicted stress intensity factor (KI) at the crack center (ie, at the tip of the minor axis) with respect to elapsed time for type 304 stainless steel in a boiling water reactor environment at 288
C [38].

both axes results in the predicted crack lengths shown in Fig. 6.30(a). The increase in the major axis length is substantially greater than that along the minor axis. Also contained in this figure is the predicted impact of the increase in KI at the tip of the minor axis. This contribution is negligible compared with that caused by the effect of increasing ECL, from which it is concluded that the development of semielliptical cracks is primarily an electrochemical phenomenon. Finally, the evolution of the crack shape, as calculated using Eqs. [6.4]e[6.6], is displayed in Fig. 6.30(b). The initial crack nucleus was assumed to be semicircular, so that the development of the semielliptical shape of a surface crack is a direct result of the divergence in the CGRs along the two axes. The rate of evolution of semielliptical cracks depends on those variables that affect the CGR, including oxygen concentration and hence ECP, conductivity, and stress intensity factor, among others. The impact of [O2]/ECP on crack shape is shown in Fig. 6.31. In examining these graphs, bear in mind that different length scales are used in the different graphs. Thus, for the lowest oxygen concentration of 1 ppb, corresponding to an ECP < Ecrit, the crack grows little and retains the shape of the semicircular nucleus. In this case the crack growth rate along the two axes is the same. As the concentration of oxygen and hence the ECP increases above the critical potential for IGSCC in sensitized type 304 SS in high-temperature water, the cracks are predicted to not only grow in size, but also progressively become more

The electrochemical nature of stress corrosion cracking

279

(a) 0.20 Crack growth direction Lmajor Lminor

Crack length, L (cm)

0.15

Lminor w/o increase in KI Conductivity: 0.11 μS/cm KI: 25.0 MPa √m Flow velocity: 100 cm/s (O2): 100 ppb

0.10

T: 288ºC

0.05

0

0

200

400 600 Time, t / h

800

1000

(b) 0.10 With increase in KI Without increase in KI

0.08

Lminor (cm)

Conductivity: 0.11 μS/cm

0.06

KI: 25.0 MPa √m Flow velocity: 100 cm/s (O2): 100 ppb T: 288ºC

0.04 Crack advance

0.02

0

–0.04

–0.02

0 Lmajor (cm)

0.02

0.04

Figure 6.30 Evolution of crack lengths along the major and minor axes (a) and a semicircular crack in a metal surface (b) [38].

10

I

T: 288ºC (O ): 10 ppb 2

80

Flow velocity: 100 cm/s

60

Conductivity: 0.11 μS/cm

Time (h) 0 2.8 5.6 11.1 16.7 22.2 27.8

1.0

Lminor (μm)

15

K : 25 MPa √m

100

Lminor (μm)

20

Conductivity: 0.11 μS/cm

Time (h) 0 I 2.8 T: 288ºC 5.6 (O ): 1 ppb 2 11.1 Flow velocity: 100 cm/s 16.7 Crack advance 22.2 27.8

Crack advance

40

0 –15 –10 –5 0 5 Lmajor (μm)

10

0 –60 –40 –20 0 20 Lmajor (μm)

15

40

50

10 0.4 0.3 0.2 0

6

4

2

0

40

0.1 –4

–2

0

Time (h) 0 2.8 5.6 11.1 16.7 22.2 27.8

–4

2

4

Conductivity: 0.11 μS/cm

Lminor (mm)

Lminor (mm)

8

30

20

K : 25 MPa √m I

T: 288ºC (O ): 1 ppm

10

2

Flow velocity: 100 cm/s

–2

0 Lmajor (mm)

2

I

T: 288ºC (O ): 100 ppb 2

Flow velocity: 100 cm/s

0.6 0.4

Time (h) 0 2.8 5.6 11.1 16.7 22.2 27.8

Crack advance

0.2

20

5

0.8

K : 25 MPa √m

4

0

0 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 Lmajor (μm)

60 2.5 2.0 1.5 1.0 0.5 0

–20

Time (h) 0 2.8 5.6 11.1 16.7 22.2 27.8

–20

–10

0

10

20

Conductivity: 0.1 μS/cm K : 25 MPa √m I

T: 288ºC (O ): 10 ppm 2

Flow velocity: 100 cm/s

–10 0 10 Lmajor (mm)

20

Figure 6.31 Predicted crack shape with respect to time elapsed and as a function of electrochemical potential for type 304 stainless steel (SS) in boiling water reactor primary coolant (water at 288
C). Lmajor and Lminor represent the crack length along and perpendicular to the surface, respectively [38]. The electrochemical corrosion potential (ECP) values for oxygen concentrations of 1 ppb, 10, 100, 1, and 10 ppm are calculated to be 0.6025, 0.1987, 0.0818, 0.024, and 0.1259 Vshe, respectively.

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

Lminor (μm)

25

1.2

120

Conductivity: 0.11 μS/cm

K : 25 MPa √m

280

30

The electrochemical nature of stress corrosion cracking

281

semielliptical in form. The increase in size is an important issue because if the growth of the semielliptical cracks was caused by mechanical fracture (eg, at a creep rate of 1.6  1010 cm/s; Fig. 6.4), the sizes of surface cracks cannot, in practice, be accounted for. The predicted impact of solution conductivity and stress intensity factor at an oxygen concentration that yields a corrosion potential (0.0818 Vshe) that is well above the critical potential for IGSCC (0.23 Vshe), and hence where electrochemical effects should dominate, are shown in Fig. 6.32(a) and (b), respectively. The effect of conductivity is predicted to be profound because of the greater throwing power of the current from the crack mouth, such that a larger area is available to reduce the oxygen depolarizer. This results in a larger coupling current and hence in a higher CGR. The impact of KI is predicted to be not so profound, no doubt because the crack growth rate in the stage II region of the CGReversusestress intensity factor correlation is only weakly dependent upon KI.

6.7

Validation of the coupled environment fracture model

It is axiomatic in the modeling of physicochemical systems that the models should be validated against experiments using data that were not used in the initial calibration. Unfortunately, this is a much-violated constraint because it is often apparent that the predictive veracity of a model is determined by comparison of the predicted CGR against the same data that were used for calibration. Furthermore, the CGR data for IGSCC in sensitized type 304 SS in BWR primary coolant (pure water at 288
C) display such an apparently large scatter (Fig. 6.33) that ensures that virtually any model can be validated. Although it is shown below that the scatter is not as severe as that indicated in Fig. 6.34, since much of the apparent scatter is due to the inherent difficulty of representing multifunctional data in a two-dimensional plot. Thus it is known that the dependent variable (the CGR) is a function of at least six variables (temperature, KI, ECP, DoS, k (conductivity), flow velocity, and pH); considering the possible interactions between these independent variables, a very complex problem of characterizing the fracture process becomes apparent. Problems of this type are most effectively analyzed using artificial neural networks (ANNs) in the pattern recognition mode [49], which is designed to uncover hidden relationships between dependent and independent variables. The weights of these relationships can be used to characterize the “character” of the phenomenon (IGSCC in sensitized type 304 SS in BWR primary coolant). By assembling as large a database as possible from data reported in the open literature, Shi and Macdonald [34,51] developed the ANN shown in Fig. 6.35 to derive the character of the fracture process. In developing the database, one of the most challenging problems was to overcome the sparse nature of the data matrices. Sparseness resulted from many authors failing to report key independent variables in their experiments. While most authors reported the temperature and stress intensity factordno doubt because most measurements were made in the mechanical/nuclear engineering communitydand many reported the

282

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

(a)

40

Lminor (mm)

30

Conductivity (μS/cm) 0.4 0.06 0.11 0.3 0.34 0.62 0.2 1.75

11.1 h 5.6 h 2.8 h

11.1 h 5.6 h

0.1

2.8 h

11.1 h 5.6 h

0

20

2.8 h

–0.2 –0.1

T: 288ºC (O2 ): 100 ppb

0

0.1

0.2

Flow velocity: 100 cm/s 10

K I: 25 MPa √m 2.8 h

11.1 h 0 40

(b)

0 Lmajor (mm)

–20

–40

1.2

1.0

0.8 Lminor (mm)

20

5.6 h

Conductivity: 0.11 μS/cm T: 288ºC (O2): 100 ppb Flow velocity: 100 cm/s t: 11.1 h Stress Intensity Factor 5 MPa √m

0.6

15 MPa √m 25 MPa √m

0.4

35 MPa √m 45 MPa √m

0.2

0 –0.6

–0.4

–0.2

0

0.2

0.4

0.6

Lmajor (mm)

Figure 6.32 Predicted evolution of a semielliptical crack in sensitized type 304 stainless steel as a function of solution conductivity (a) and stress intensity factor (b) [38].

The electrochemical nature of stress corrosion cracking

283

Measured crack growth rate (cm/s)

10–6 10–7 10–8 10–9 10–10 10–11 10–12

–0.6

–0.4

–0.2

0.0

0.2

0.4

0.6

ECP (Vshe)

Figure 6.33 Summary of crack growth rate as reported in the literature versus corrosion potential for type 304 stainless steel in boiling water reactor primary coolant [48].

oxygen concentration, few reported the ECP, conductivity, pH, or DoS of the steel. The ECP is readily calculated using the mixed potential model [50], and the conductivity and pH could be estimated satisfactorily from the composition of the solution and the known temperature [9]. A few studies reported measured values for the DoS in terms of the electrochemical polarization reverse (EPR) value (C/cm2), though many simply referred to the steel as being “sensitized” and often reported only sensitization temperature and time data. In these cases, provided that the sensitization conditions were reasonably “standard,” an EPR value of 15 C/cm2 was assigned. The ANN developed in this work was trained by the back propagation/error minimization method using half of the database, with the remaining half being used to assess the performance of the net. The net itself comprised five layers of neurons: one input layer, one output layer, and three hidden layers. The neurons in each layer are connected to all of the neurons in the preceding and following layers, as shown in Fig. 6.34(a). Each neuron has two functions: First, the input signals from the preceding neurons are summed and adjusted using a bias, and then the summed signal is subjected to a transfer function, as illustrated in Fig. 6.34(b). The transfer function is commonly an “on/off” switch, which passes the information to the following layer if some condition is met (eg, the magnitude exceeds a preset value), but in this net a sigmoid transfer function that could operate with varying degrees of being “on” or “off” was used. This imbues the ANN with a certain “fuzziness,” which is advantageous in handling imprecise data, such as those used in this study. The neurons in successive layers are connected by synapses that are characterized by unique weights. Thus, in the training process, an initial set of weights is assumed, the net is exposed to a

284

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

(a)

Input layer

Output layer

Hidden layers

Output variable

Input variables

Neurons

(b) Inputs from the previous state

Σ f

Output

n

yk = f (bk + Σ Wk,i Xi ) (l )

(l )

(l )

(l )

i=1

Bias term

(c) T (°C)

KI (MPa √m)

Conductivity (μS/cm)

ECP (Vshe)

EPR (C/cm2)

pH

CGR (cm/s)

Figure 6.34 (a) The topology of the artificial neural network (ANN) used in assessing the veracity of the coupled environment fracture model for predicting crack growth rate (CGR) in sensitized type 304 stainless steel in boiling water reactor primary coolant. (b) Schematic of each neuron in the network. S signifies summation, whereas f represents the transformation (sigmoid function). (c) Summary of the independent variables used in the ANN [34]. T, temperature; KI, stress intensity factor; ECP, electrochemical corrosion potential.

set of independent variables (Fig. 6.34(c)), and an output is calculated. This output is compared with the known dependent variable (CGR) from the evaluation set of data and any difference is noted. This error is then propagated back through the net, and the weights of the synapses between neurons are adjusted to reduce the error on the subsequent forward calculation. This process is continued cyclically until satisfactory convergence is obtained. Typically, tens of thousands of cycles are required, but in more difficult cases the number of cycles can exceed 100,000 or even 1 million. The process has often been likened to training a child in some task, and well it should be, because an ANN emulates the processes that occur in the brain, with memory being the establishment of weights between neurons. Once trained, the ANN becomes a powerful prediction tool in its own right because of the definition of the hidden relationships between the dependent and independent variables. However, it is important to note that the net contains no preconceived model and hence is purely empirical in nature. Accordingly, an ANN cannot directly provide mechanistic information, but can be used to define the “character” of a phenomenon (eg, crack growth), noting that a successful model/mechanism must be able to reproduce that character.

The electrochemical nature of stress corrosion cracking

285

Log ANN-predicted CGR (cm/s)

–6

–7 95% confidence –8

–9

95% confidence

–10 ⫾0.4 log units

–11 –11

–10

–9

–8

–7

–6

Log measured CGR (cm/s) Figure 6.35 Plot of crack growth rate in sensitized type 304 stainless steel in boiling water reactor primary coolant (water at 288
C) as predicted by the artificial neural network (ANN) (a) versus that of the evaluation data set (b) [34].

The output of the ANN that was trained on the “training” set of data (50% of the total database) is plotted in Fig. 6.35 against the measured data. The plot has a gradient of 1, showing that the predictions of the trained ANN are in high fidelity with those of the experiment and that the inherent accuracy of the data is 0.4 log unit. This is the accuracy with which the ANN may be used to predict CGR under any given set of the selected independent variables. Plots of the CGR predicted by the ANN and by the CEFM as a function of ECP for the conditions indicated in the figure are shown in Fig. 6.36(a) and (b), respectively. Although there are slight differences in conductivity, the principal differences are that the ANN predicts that the crack should remain active at ECP values as low as 0.6 Vshe at the higher conductivities, whereas the CEFM predicts that the creep limit is reached at ECP values that are more negative than ca 0.4 Vshe at the highest conductivity. However, the ANN predicts that the conductivity does not have a significant impact on CGR at ECP values >0.3 Vshe, whereas the CEFM does predict a significant impact. It is important to note, however, the paucity of data at high and low potentials, which makes effective training in these regimes problematic. Both the ANN and the CEFM predict a significant impact of conductivity on the stress corrosion CGR, which is attributed to enhanced throwing power of the current from the crack mouth, such that a larger area is available for oxygen reduction, resulting in a larger coupling current and hence CGR.

286

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

(a) ANN-predicted crack growth rate (cm/s)

10–7 T = 288ºC KI = 27.5 MPa √m

pHT = 5.67 EPR = 15C/cm2 10–8

10–9

4.15 μS/cm 3.9 μS/cm 3.46 μS/cm Experimental

10–10 –0.6

–0.4

–0.2

0.0

0.2

0.4

ECP (V vs SHE)

CEFM-predicted crack growth rate (cm/s)

(b)

10–7

KI = 27.5 MPa √m

pHT = 5.67 T = 288ºC EPR = 15C/cm2

10–8

3.46 μS/cm 2.92 μS/cm 2.65 μS/cm Experimental

10–9

10–10 –0.6

–0.4

–0.2 0.0 ECP (V vs SHE)

0.2

0.4

Figure 6.36 Dependence of crack growth rate on electrochemical corrosion potential (ECP) as predicted using the artificial neural network (ANN) for different values of the stress intensity factor (KI) and degree of sensitization (a). (b) Experimental data with conductivity (k) values between 0.06 and 0.4 mS/cm at ambient temperature. The conductivities shown in the figure correspond to those calculated for 288
C [48].

The electrochemical nature of stress corrosion cracking

287

The impact of the DoS coupled with ECP on CGR in sensitized type 304 SS in BWR primary coolant (water at 288
C) as predicted by both the ANN and the CEFM is displayed in Fig. 6.37(a) and (b), respectively. Both models predict sigmoid dependencies of CGR on EPR, with the CGR increasing by about a factor of 10 when the EPR is increased from 0 C/cm2 (unsensitized) to 30 C/cm2 (fully sensitized). The ANN predicts a lower impact of ECP (cf Fig. 6.37), no doubt again reflecting a paucity of data. The impact of stress intensity factor on CGR, coupled with the impact of ECP as predicted by the ANN and the CEFM, is displayed in Fig. 6.38. The principal differences between the ANN and CEFM predictions are the greater dependence of the CGR on KI predicted by the ANN (although these differences are, for the most part, within the accuracy of the data as indicated in Fig. 6.35) and the apparent failure of the ANN to predict KISCC. The failure on the part of the ANN to predict the existence of KISCC is again attributed to a lack of data, because few measurements of CGR have been reported for KI < 10 MPa Om. To assess the ability of the CEFM to reproduce the character of IGSCC in sensitized type 304 SS in BWR primary coolant (water at 288
C), we used the CEFM to create a database of CGR versus ECP, DoS, temperature, KI, conductivity (k), and pH covering the same ranges of these independent variables in the experimental database. These data then were used to train the ANN in exactly the same manner that was used to train the net on the experimental data; the character of the CEFM was derived as described by Shi et al. [34,51]. The results are displayed in Table 6.5. This comparative analysis of the ANN versus the CEFM shows that the CEFM reproduces the “character” of IGSCC in sensitized type 304 SS in BWR primary coolant with great fidelity with respect to the experimental data. However, the match is not perfect; the following differences are noted: • • • • •

The CEFM The CEFM The CEFM The CEFM The CEFM

overestimates the importance of the stress intensity factor. slightly underestimates the importance of temperature. slightly underestimates the importance of conductivity. significantly underestimates the importance of ECP. slightly overestimates the importance of the DoS.

Nevertheless, the character predicted by the CEFM closely matches that indicated by the ANN for IGSCC in sensitized type 304 SS in BWR primary coolant. To my knowledge, this is the first such analysis ever performed. Accordingly, we lack data on determining a priori how significant these differences might be. Future developments of the CEFM will aim at reducing these differences. Similar results were found for Alloy 600 in PWR primary coolant [51]. In any event, both the CEFM and the ANN demonstrate that IGSCC in this steel/environment system is primarily electrochemical in nature (ECP, conductivity), augmented by mechanics (KI) and metallurgy (DoS). Interestingly, the CEFM seems to significantly underestimate the electrochemical component of the character, in spite of the fact that the CEFM is strongly based in electrochemistry. Future work will review all aspects of the CEFM with the goal of reducing the character difference noted above.

288

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

ANN-predicted crack growth rate (cm/s)

(a)

10–6

10–7

10–8

10–9

T = 288ºC

ECP 100 mVshe

KI = 27.5 MPa √m

ECP –50 mVshe

κ = 5.1 μS/cm pHT = 5.67

10–10

0

5

10

(b)

ECP –100 mVshe Experimental

15 20 EPR (C/cm2)

25

30

35

CEFM-predicted crack growth rate (cm/s)

10–6

10–7

10–8

10–9

10–10

T = 288ºC

ECP 100 mVshe

KI = 27.5 MPa √m

ECP –50 mVshe

κ = 5.1 μS/cm pHT = 5.67 0

5

10

15

ECP –100 mVshe Experimental 20

25

30

35

EPR (C/cm2)

Figure 6.37 Comparison of the dependencies of crack growth rate (CGR) in type 304 SS in BWR primary coolant on EPR for different values of the electrochemical corrosion potential (ECP), as predicted by the artificial neural network (ANN) (a) and the coupled environment fracture model (CEFM) (b) for a stress intensity factor (KI) of 27.5 MPa Om, conductivity (k) of 5.1 mS/cm, and pHT of 5.67. The conductivities shown in the figure correspond to those calculated for 288
C [34].

Finally, it is worth assessing how accurately the CEFM can predict CGR in sensitized type 304 SS in BWR primary coolant. This is best done by comparing the CGRs predicted by each code for the same set of conditions, with the sets corresponding to those used in training the ANN (see Table 6.5). The comparison is shown in Fig. 6.39.

The electrochemical nature of stress corrosion cracking

289

Crack growth rate (cm/s)

10–7

10–8

10–9

ANN (ECP = 30 mVshe) ANN (ECP = –100 mVshe)

10–10

10–11

ANN (ECP = –200 mVshe)

T = 288ºC κ = 5.15 μS/cm pHT = 5.67 EPR = 15C/cm2

CEFM (ECP = 30 mVshe) CEFM (ECP = –100 mVshe) CEFM (ECP = –200 mVshe) Experimental

10–12 10

20

30 KI (MPa √m)

40

50

Figure 6.38 Comparison of the dependencies of crack growth rate on stress intensity factor (KI) for different values of the electrochemical corrosion potential (ECP) for intergranular stress corrosion cracking in sensitized type 304 stainless steel in boiling water reactor primary coolant (water at 288
C), as predicted by the artificial neural network (ANN) and the coupled environment fracture model (CEFM) [34].

Comparison of the “character” of intergranular stress corrosion cracking in sensitized type 304 stainless steel in boiling water reactor primary coolant (water at 2888C)

Table 6.5

Range

Character, ANN (%)

Character, CEFM (%)

10.4e67.7

10.8 (M)

15.1

25e292

17.8 (E)

15.4

0.52e5.72

14 (E)

12.4

0.575 to þ0.496

43.6 (E)

25.9

Degree of sensitization (C/cm )

0e33.79

13.8 (M)

19.6

pH

5e8

e

11.6

Variable Stress intensity factor (MPa Om) Temperature

(
C)

Conductivity (mS/cm) Electrochemical potential (Vshe) 2

ANN, artificial neural network; CEFM, coupled environment fracture model. Reproduced from Shi et al. [34].

The 95% confidence limits correspond to 0.4 log unitdthe same level of uncertainty as found for the ANN (Fig. 6.35). This is the origin of my often derided conclusion that the CGR in sensitized type 304 SS in BWR primary coolant can be as accurately calculated as measured by using the CEFM.

290

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

Log (CEFM-predicted CGR, cm/s)

–6

–7

95% confidence

–8

95% confidence

–9

–10

–10

–9

–8

–7

–6

Log (ANN-predicted CGR, cm/s)

Figure 6.39 A comparison of ANN-predicted crack growth rate (CGR) and coupled environment fracture model (CEFM)-predicted CGR.

6.8

Summary and conclusions

The importance of coupling between the internal and external environments of propagating cracks in sensitized type 304 SS in simulated BWR coolant environments at 288
C, in thiosulfate-containing solution at 22
C, and for the intergranular fracture of AISI 4340 steel in 6 M NaOH at 70
C, has been examined by measuring the coupling current that flows between the crack and the external surface, where it is consumed by the reduction of a cathodic depolarizer (eg, oxygen). Coupling is the necessary condition that is required to sustain differential aeration and hence localized corrosion, and it provides an opportunity to examine the nature of the processes that occur at the crack tip from the “noise” contained in the current. The findings of this work can be summarized as follows: •

•

The coupling current consists of quasi-periodic oscillations (“noise”) superimposed upon a mean. The noise contains valuable mechanistic information that is postulated to arise from fracture events that occur at the crack tip, as well as from repassivation of the exposed metal of historical events on the crack flanks as they become progressively more distant from the crack tip. In the case of fracture in sensitized type 304 SS in simulated BWR coolant at 288
C, the oscillations are resolved into packages of 4 to 13 that are separated by short periods of low amplitude (intense activity). These data are consistent with fracture occurring event by event and grain by grain across the crack front, progressing up (or down) a crack face that is less than favorably oriented with respect to the applied stress. When the crack intersects a grain boundary that is favorably oriented, the boundary “unzips,” thereby producing a

The electrochemical nature of stress corrosion cracking

•

•

•

•

•

291

brief period of high-frequency noise. For intergranular fracture in the same alloy in thiosulfate solution, and for intergranular fracture in AISI 4340 in caustic solution, the data are consistent with many microfracture events occurring more or less simultaneously across the crack front. When corrected for the difference in temperature, the microfracture frequency observed in the thiosulfate solution is consistent with that observed in BWR primary coolant as calculated using the known activation energy (40 kJ/mol) for strain rate in sensitized type 304 SS. However, through the judicious choice of NaOH concentration, the fracture events occurring in AISI 4340 steel in 6 M NaOH at 70
C can be temporally resolved, thereby allowing examination of the kinetics of individual events. The repassivation process is found to be of the first order in kinetic character, and a first-order plot produces a rate constant that depends on the rolling direction of the steel from which the C(T) specimen was machined. Although only few data are available, the CGR in sensitized type 304 SS in high-temperature (250
C), dilute sulfate solution seems to be linearly related to the coupling current, in agreement with the predictions of the CEFM. This relationship possibly provides an extraordinarily sensitive method for monitoring CGR because of the ability to measure very small currents. Coupling between the internal and external environments, as embodied in the CEFM, leads to the prediction that the CGR will decrease as the crack depth increases. This relationship, which is an analytical consequence of charge conservation and arises because of the increase in IR potential drop down the crack, which subtracts from the potential drop that is available on the external surface to drive the oxygen reduction reaction, has enormous implications for the rate of accumulation of localized corrosion damage. Modification of the chemical and electrochemical properties of the external environment, including the external surfaces upon which the coupling current is consumed, is predicted and found experimentally to have a profound impact on the rate of crack growth. For example, the CEFM predicts that increasing the specific impedance of the external surface, resulting in a decrease in the exchange current density for the reduction of oxygen (which consumes the coupling current that flows from the crack mouth), will decrease the CGR. This prediction is found to hold for the IGSCC in sensitized type 304 SS in high-temperature (250
C), dilute sulfate solutions; the reduction in the exchange current density is affected by the deposition of a ZrO2 coating on the external surfaces (and only on the external surfaces). This observed reduction in the CGR is in excellent accord with the predictions of the CEFM. On the other hand, catalyzing the oxygen reduction reaction on the external surfaces increases the CGR because of the increased ability of the surfaces to consume a larger coupling current. In all three cases, crack growth is considered to be more consistent with a hydrogen embrittlement mechanism than with the classical SDR mechanism, primarily on the basis of the dimension of the microfracture events that occur at the crack tip. Thus, if the SDR mechanism occurred, the fracture dimension should be some small multiple of Burgers vector, corresponding to a (small) finite number of slip planes in a slip band at the crack tip, and hence should be of the order of tenths of nanometers in dimension. Instead, the fracture events are found to be micrometer to hundreds of micrometers in dimension, corresponding to subgrain to supergrain sizes. The only mechanism that seems to be consistent with these results is HIC, although dealloying may be a viable candidate. The use of the CEFM for calculating the ECP and the CGR for a “standard crack” in any component in the primary coolant circuit of a BWR operating at any specified power under different water chemistry protocols has been demonstrated. The predictions illustrate the impact that electrocatalysis and electroinhibition have on the accumulated damage, and

292

•

•

Stress Corrosion Cracking of Nickel-based Alloys in Water-cooled Nuclear Reactors

provide a theoretical basis for assessing and designing strategies for the mitigation of SCC in operating BWR power plants. The predictions with respect to inhibition have been demonstrated in laboratory studies, whereas those for catalysis have been demonstrated in the field in the form of HWC/noble metal chemical additions in the field. The CEFM provides an alternative explanation for the shape of cracks in plane surfaces (semielliptical surface cracks), as follows: The evolution of the shape of surface cracks depends on ECP, stress intensity factor (KI), and solution conductivity in sensitized type 304 SS in BWR environments. Local stress intensity factor along the crack front has little impact on the evolution of crack shape, but it is not superior to that of environmental variables. The ability of the CEFM to predict CGR in high-temperature aqueous systems has been evaluated using an ANN to derive the character of IGSCC in sensitized type 304 SS by training the net of a database developed from CGR data reported in the literature and based on an identical database developed from the predictions of the CEFM. The “character” of IGSCC in both cases was defined as the contribution that each independent variable (temperature, ECP, KI, conductivity, pH, and so on) makes to the dependent variable (CGR). The weights are calculated from the weights of the synapses (connections) between the neurons. Comparison of the characters demonstrates that the CEFM is capable of reproducing IGSCC in sensitized type 304 SS in BWR environments with high fidelity. A direct comparison of the CGRs predicted by the ANN and the CEFM supports the conclusion that the CEFM is capable of predicting CGR at least as accurately as it can be measured.

Acknowledgments The author gratefully acknowledges the support of this work by the Department of Energy/ Environmental Management Science Program under grant no. DE-FG07-97ER62515, the Department of Energy/Nuclear Energy Education Research Program under grant no. DE-FG07-021D14334, and the Department of Energy/Nuclear Energy Research Initiative under grant no. DE- FG03-021D-22618. Finally, the author gratefully thanks Dr. Sang-Kwon Lee for the preparation of Figs. 6.14e6.16.

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