A crack size dependence of environmentally assisted crack growth rate based on electrochemical differences between small, short and long cracks is well established (Gangloff, 1981; Eickemeyer, 1987; Lee et al., 1988; Nakai et al., 1989; Jones & Simonen, 1994; Berechid et al., 1999; Nakajima et al., 2001; Kim & Hartt, 2006; Burns, 2010; Turnbull, 2012; Zhou et al., 2015). There is confusion in the literature regarding the concept of small and short cracks, with the term short crack being used often for both through-thickness cracks of short crack length in fracture mechanics specimens and small surface cracks emerging from defects, notches or corrosion pits. Here, we use the term small crack for a surface crack, emerging from a pit in this case, and the term short crack exclusively for a crack in a fracture mechanics specimen. Most studies of crack size effects on growth rate have been in highly conductive solution, but as highlighted in the review by Turnbull (2012), crack size effects may be more likely in low conductivity solutions because of the significant difference in potential drop in a small or short crack compared to a long crack. Indeed, in the work of Gangloff (1981) on high-strength low-alloy steel in 3.5% NaCl, the potential drop in the crack was a key feature (Turnbull & Ferriss, 1986) and not just crack chemistry as proposed by Gangloff, although the two are intrinsically linked.
An application where low conductivity solutions are prevalent in service is in power generation by steam turbines. For these, the inlet feedwater under well-controlled conditions has anion concentrations of a few ppb (by mass). Partitioning into the condensate can mean that these anions concentrate up to about 300 ppb (Zhou & Turnbull, 2003). Nevertheless, control of water chemistry is seldom ideal, and excursions in anion conductivity to varying extent will arise.
Extensive measurements to characterise the corrosion fatigue and stress corrosion crack growth rates of long cracks in 12Cr steam turbine blades have been made (Turnbull & Zhou, 2010, 2011) to compare relative materials performance and inform inspection planning. However, to estimate overall life and the time to develop to a detectable crack, it is necessary to quantify the growth rate of the crack at different length scales, and this has been the focus of our recent research. The primary test environments have been 300 ppb Cl− and 300 ppb SO42− to represent normal water chemistry (Zhou & Turnbull, 2003) and 35 ppm Cl− to reflect a typical excursion. Testing was conducted with a FV566 12Cr martensitic stainless steel under full immersion conditions at 90°C, corresponding approximately to the temperature of first condensation. The relative merits of full immersion versus steam condensing conditions have been discussed previously (Turnbull, 2008). In essence, full immersion allows control of chemistry and measurement of potential. While testing in condensing steam may seem more realistic, there is considerable uncertainty as to the nature of the condensate chemistry in the laboratory when varying boiler chemistry and also its relationship to service condensate chemistry for the same nominal boiler chemistry. Some turbine manufacturers test their materials in full immersion, while others test under condensing steam conditions. There is no ideal approach. The implication of the increased potential drop associated with a thin liquid layer is discussed later in relation to modelling crack electrochemistry. For long cracks (6 mm or greater), compact tension specimens were used; for short cracks with initial dimension of the order of 100 μm, through-thickness single edge-cracked tension specimens; for small cracks, the crack was grown from a corrosion pit generated electrochemically to a controlled depth in a flat dog-bone specimen.
The extent of aeration of the condensate solution is a key factor in determining the damage mechanism, as pitting and stress corrosion cracking of blade steel will occur only in aerated solution. Aeration occurs off-load and during start-up, with the effect of oxygen on corrosion prevailing for about 24–48 h following start-up. At long times, the turbine chamber should become oxygen-free, although leakage via the seals may allow ingress on rare occasions. Failure of blades is commonly by high cycle fatigue (most often from corrosion pits formed off-load), but there is considerable uncertainty about the impact of low-frequency high-amplitude fatigue associated with regular start-up and shut-down, the latter increasingly being adopted to balance out fluctuating demand associated with electricity from renewable energy. One consequence of such regular cycling is that the chamber may remain aerated for long periods, which has implications for corrosion fatigue crack growth rates and the superposition of stress corrosion cracking.
The aim of this paper is to focus only on the key results from disparate pieces of research, the fine details of testing being described by Zhou et al. (2015) and Turnbull & Zhou (2017) and the modelling by Turnbull & Wright (2017). The primary goal is to present a coherent scientific framework to interpret the results and to draw inferences for the mechanism of crack growth.
2 Summary of experimental data
2.1 Corrosion fatigue
Figure 1 summarises the growth rate measurements for long cracks in aerated and deaerated 300 ppb Cl− and 300 ppb SO42−, together with data from tests in aerated 35 ppm Cl−. At these very low loading frequencies, the growth rate was measured at a specific K value; this stress intensity factor was then stepped to a larger value and so on. In 300 ppb Cl− and 300 ppb SO42−, the crack growth rate was the same in aerated solution (E=−0.15 V SCE) and deaerated solution (E=−0.6 V SCE). Surprisingly, the growth rate in 35 ppm Cl− was similar to that in the lower conductivity environment with perhaps a lower threshold ΔK, although the data are too limited to be sure.
The solution in the crack will be oxygen-free, as oxygen reduction is a fast reaction and replenishment at this low loading frequency is slow. Hence, in the absence of any stimulation from the external surface, the crack-tip potential will tend to adopt the potential for deaerated solutions, about −0.6 V (SCE). In practice, the crack-tip potential is likely to be more negative than this under fatigue loading, as the increased anodic activity associated with production of film-free surface at the crack tip during rising load must be balanced by an increase in the local cathodic kinetics and that requires a decrease in electrode potential. Experimental evidence for such an effect was demonstrated for a steam turbine disc steel by challenging crack-tip potential measurements in very low conductivity solution (Turnbull et al., 2004).
The absence of any effect of aeration on the crack growth rate in 300 ppb Cl− and 300 ppb SO42− (Figure 1) implies that the potential drop between the external surface remote from the crack mouth and the crack tip is so large for the long crack that the crack tip is effectively decoupled from the external surface, despite a corrosion potential of −0.15 V (SCE). In view of the low solution conductivity and length of the crack (which determines the total current), this is not a surprising observation but the similarity of the growth rates for the two test solutions suggests that this decoupling extends also to 35 ppm Cl−. Testing is underway at higher chloride concentrations to further elucidate the dependence of crack growth and related coupling between the crack tip and external surface on solution conductivity (see later discussion on modelling results).
The conceptual expectation is that the potential drop should be lower as the crack length gets shorter, and this should induce some crack-tip anodic polarisation in aerated bulk solution. This is reflected in the enhanced crack growth rate for short cracks relative to long cracks in Figure 2 but the absence of such effect in deaerated solution. The tendency to have a lower threshold ΔK for this case most likely reflects reduced crack-tip shielding relative to that for the long crack in aerated solution. Unfortunately, there are no data for long crack growth in deaerated solution near threshold for a more direct comparison of crack size effects on shielding.
In aerated solution, the transition from short to long crack growth rates occurs at a crack length of about 250 μm or so, implying that crack-tip polarisation in this low conductivity solution is constrained to relatively short crack lengths. However, it is apparent from Figure 2 that this enhanced growth rate does not prevail for small cracks grown from corrosion pits, despite the small crack depth. The deduction is that the additional current flowing from the pit, even though the pit is passive in this solution, just limits crack-tip polarisation. It could be postulated that the growth rate of the small crack near the mouth ought to be greater as the potential drop in that location should be smaller. This should cause the crack to grow faster at the surface and the crack shape to change. In practice, this was not observed in both respects and may indicate that the potential drop external to the crack remained a major factor limiting polarisation.
In Figure 1, the data for 35 ppm Cl− indicated no apparent influence of chloride ion concentration on the growth rate for long cracks, although perhaps some effect on threshold ΔK. Nevertheless, it would be expected that acceleration of the growth rate should occur for a small crack at this higher concentration simply because of the reduced potential drop (smaller total current and higher conductivity). The results of such testing are shown in Figure 3 (in this case, no equivalent tests with short cracks were possible). For the small crack, the threshold ΔK in 35 ppm Cl− is similar to that for the 300 ppb Cl− and 300 ppb SO42− solution. Above the threshold, there is distinct variability in the results, with two tests in 35 ppm Cl− generating growth rates similar to that for the long crack and one test resulting in significantly accelerated growth. This variability in results for the same environment could not be explained by differences in initial crack depth, which were broadly similar. In the test with the enhanced growth rate, the crack growth rate was up to five times that for the other tests with the accelerated growth extending to a crack depth of 1.5 mm. Examination of the fracture surface showed that the cracking mode in this case was intergranular, and crack shape was more elliptical, with long axis in the depth direction, while those for all other tests indicated a transgranular mode of cracking and a tendency to be semi-circular in shape.
2.2 Stress corrosion cracking
Stress corrosion crack growth rates were determined in 35 ppm Cl− for long, short and small cracks. The threshold stress intensity factor in 300 ppb Cl− and 300 ppb SO42− was measured previously to be about 42 MPa m1/2 (Turnbull & Zhou, 2010). This stress intensity factor is not readily achievable for a short or small crack without gross yielding. Hence, results are shown only for 35 ppm Cl− in Figure 4. The threshold stress intensity factor was about 15–16 MPa m1/2 for both short and long cracks, but the growth rate for the short cracks was up to 20 times that for the long crack. For small cracks, the growth rate was more variable and somewhat greater than that for the short crack. In all cases – long, short or small cracks – the cracking was intergranular.
One feature of these results was the increase in growth rate, relative to the long crack, for the short crack even when the latter was about 1.6 mm. Conceptually, a transition to a long crack growth rate is expected as the crack length increases. Unfortunately, a combination of longer crack length and small K value is not achievable for the through-thickness edge-cracked specimen geometry adopted. Hence, to provide insight, a compact tension specimen was tested with an initial crack length from the notch root of 1 mm, instead of the usual value of 6 mm adopted for long cracks. The results in terms of growth rate versus crack length (depth for small cracks) together with those from Figure 4 are represented in Figure 5. Although only one result from the short crack compact tension testing has been obtained and appropriate caution should be applied, the results show a remarkable decaying growth rate between about 1.5 mm and 2 mm.
3 Summary of modelling results
The details of the crack electrochemistry modelling are described elsewhere (Turnbull & Wright, 2017). The essential features are as follows:
- anodic (Fe and Cr atom dissolution) and cathodic (H+ and H2O reduction) reactions in the crack;
- hydrolysis of ferrous ions and of chromium ions;
- solubility limit for Fe2+ in relation to Fe(OH)2;
- crack-tip active or passive, crack walls passive;
- oxygen reduction external to crack;
- steel in passive state on external surface;
- potential drop external to the crack calculated from solution to Laplace equation.
The effect of cyclic loading was not considered at this stage of model development, although the results from the static crack will still provide insight. A trapezoidal crack geometry was assumed with the crack-tip opening displacement and crack-mouth opening displacement derived from standard fracture mechanics expressions assuming a through-thickness edge-cracked tension specimen. No attempt was made to replicate the more complex geometry of the small crack with a pit. There was uncertainty about the quality of the electrochemical input data so the results should be assessed principally on the trends rather than on the absolute values.
The variation of the crack-tip potential with crack length and bulk solution conductivity for a corrosion potential of −0.15 V (SCE) and K=20 MPa m1/2 is shown in Figure 6. It should be emphasised that the potential drop with respect to the externally measured corrosion potential of −0.15 V (SCE) will consist of two components: the potential drop in the crack itself and the potential drop in the low conductivity solution external to the crack. The latter occurs because the net anodic current flowing from the crack has to be balanced by an increased cathodic current on the external surface, and this means a decrease in local potential, the magnitude of which will increase with decrease in solution conductivity.
Clearly, the sensitivity of crack-tip potential to crack length increases with decreasing solution conductivity. However, to explain the response of crack growth rate to crack length, it is necessary also to consider how the chloride ion concentration and pH at the crack tip vary. The results are shown in Figures 7 and 8, respectively.
The crack-tip chloride ion concentration increases as expected with the increase in crack length and bulk chloride ion concentration with the chloride ion concentrating by ion migration in order to balance the charge associated with the dissolving metal cations. However, the response of the pH level is somewhat more complex. For bulk chloride ion concentrations of 35 ppm and greater, pH decreases with increase in crack length with little sensitivity to chloride ion concentration above 35 ppm. However, at lower concentrations, there is a minimum in pH that occurs at different crack lengths depending on the bulk chloride ion concentration. The pH level attained in a crack reflects the balance between hydrogen ion generation by dissolution and hydrolysis of metal cations (Cr3+ being the most important) and loss of hydrogen ions by cathodic reduction and diffusion. At bulk chloride ion concentrations above 35 ppm, the potential drop is small, and correspondingly, the kinetics of hydrogen ion reduction has little impact. However, for lower bulk concentrations of chloride ion, the potential drop becomes progressively more significant as the crack length increases and the resultant more negative potential in the crack then enhances the cathodic reduction reaction. This causes the pH level to increase.
4 Implications for the mechanism of crack growth
4.1 Corrosion fatigue
To date, modelling of crack electrochemistry has been applied to static cracks only. To model crack electrochemistry in corrosion fatigue cracks, it is necessary to account for the velocity of the fluid in the crack, the change in crack opening at the mouth and tip during the cycle, and in the latter case, the impact on reaction kinetics of the fresh surface produced at the crack tip. At this very low loading frequency of 4.2×10−4 Hz, the fluid velocity may be less significant compared to diffusion for cracks of length less than about 4 mm (Turnbull, 1985), but the fluctuation in crack opening means also fluctuation in potential drop during the cycle and this requires detailed computation. This will be considered for future work. Nevertheless, we can draw inferences for the corrosion fatigue behaviour from the static crack modelling.
The similarity in corrosion fatigue crack growth rates for long cracks in aerated and deaerated 300 ppb Cl− and 300 ppb SO42− solution (Figure 1) suggests that the crack-tip potential is low in both cases and associated with that of deaerated solution [−0.6 V (SCE)] or more negative. While there will be some anodic stimulus due to the production of fresh surface during loading, the dissolution rate at these low potentials is very unlikely to be sufficient to contribute to crack growth. In contrast, a low crack-tip potential, reduced further in response to generation of new surface during loading, and a cracking mode that is transgranular suggest a hydrogen-assisted fatigue mechanism of crack growth is more likely.
For the 300 ppb Cl− and 300 ppb SO42− solution, the growth rate increased with decrease in crack length (the absence of an effect for small cracks is considered due to the influence of the pit limiting polarisation; specifically, the combination of the passive current on the pit surface and that from the crack leads to a potential drop that limits crack-tip polarisation in this very low conductivity solution). The model predictions of Figures 6 and 7 indicate that the potential should become more noble and the crack-tip pH less acidic as the crack length decreases. By implication, the increase in crack growth rate for the short crack is incompatible with a hydrogen-assisted fatigue mechanism. The mechanism of crack advance has to be related to the anodic dissolution reaction directly by either a conventional slip-dissolution mechanism or a more complex anodic reaction process.
The possibility that the enhanced growth rate could be due to a superimposed stress corrosion cracking mode has to be considered. The fracture surface, after chemical cleaning, was transgranular. Also, stress corrosion cracking tests had indicated a static load threshold stress intensity factor (KISCC) of 42 MPa m1/2. While this may be reduced during rising load, it seems unlikely that it would drop to less than 12 MPa m1/2. Accordingly, we suggest that an anodic reaction enhanced fatigue process is more likely despite the implication of a change to a hydrogen-assisted fatigue mechanism as the crack length increases. The latter does not seem a radical proposal, as anodic dissolution and hydrogen generation are occurring in parallel, and it is a case of which is the more viable in accelerating fatigue crack growth.
In 35 ppm Cl−, the similarity of crack growth rate for aerated and deaerated 300 ppb Cl− and 300 ppb SO42− in long cracks (Figure 2) would suggest that for this crack size (6 mm), crack-tip decoupling prevails for this environment also, which is compatible then with a hydrogen-assisted fatigue mechanism. However, when testing with small cracks, there was significant acceleration of the crack growth rate in one test but not in two other tests. The variability suggests that the system is very close to a threshold. The cracking mode was intergranular, and KISCC in this environment is about 15 MPa m1/2. The implication is that there is a superposition of a stress corrosion cracking mode on the corrosion fatigue process (in future works, we will explore the effect of imposing a hold time on the crack growth rate, as this is of practical engineering relevance). As Figure 6 shows the potential to be more noble for a short crack (we would expect the small and short cracks to have similar trends) and the pH elevated compared to a long crack, the implication is that the accelerated growth rate compared to the long crack is associated with an intergranular anodic reaction based mechanism.
4.2 Stress corrosion cracking
For stress corrosion cracking of this 12Cr steel in low chloride solutions, it has been established that crack growth does not occur in deaerated solution (Turnbull & Zhou, 2010). The observation that crack growth occurs in aerated 35 ppm Cl− indicates indirectly that crack-tip polarisation must occur to some extent. This is in contrast to the arguments proposed to explain the corrosion fatigue data for long cracks and, by inference, highlights the importance in that case of the impact of the dynamic crack-tip opening on the total current and in reducing the local crack-tip potential to the point that there is no effect of aeration level on crack growth rate. Such a hypothesis does not negate the interpretation of the corrosion fatigue data above, as the trends would be the same; it would simply cause a shift in the magnitude of the chloride concentration required for polarisation. In contrast, modelling of the electrochemistry in a static crack with or without enhanced crack-tip dissolution kinetics associated with the stress corrosion crack growth rate (assuming a Faradaic relationship) had little impact on crack-tip potential or chemistry (Turnbull & Wright, 2017).
A key observation in Figure 4 is the large increase in growth rate for the short crack, although why the small crack should exhibit a somewhat faster growth rate for similar dimensions remains unresolved. From Figures 6 and 8, it is predicted that the shorter the crack, the more noble the potential and the higher the pH. Hence, a hydrogen embrittlement mechanism to explain the intergranular cracking process can be ruled out. An anodic reaction-controlled mechanism of crack growth based on an enhanced sensitivity of the grain boundary is implied. The long crack also exhibits an intergranular cracking mechanism, but now, the potential is lower than that for the short crack, as is the pH (Figures 6 and 7). Nevertheless, the crack-tip potential is still projected to be quite noble, about −0.25 V (SCE). Based on electrochemical data published elsewhere (Turnbull & Wright, 2017), this will tend to outweigh the effect on hydrogen generation of decreasing pH. The suggestion is that anodic reaction-controlled growth will still be the dominant process. While this seems highly likely, the model calculations of crack electrochemistry cannot be applied directly to a compact tension specimen. The potential drop external to the crack is an important factor in low conductivity solutions. The model calculations were undertaken for a through-thickness edge-cracked specimen geometry. The constraint of a deep notch to ionic current dispersion in the compact tension specimens could in principle increase the external potential drop and impact on the growth rate so that comparison of long and short cracks is not on a consistent basis, i.e. there is possibly some dependence on specimen geometry. Modelling work to resolve this was undertaken, and for very low conductivity solution, the compact tension specimen was predicted to have a lower crack-tip potential compared to the single edge notched specimen, with the effect being more significant with a crack size of 1 mm (90 mV more negative) compared to 6 mm (28 mV); for the latter, the potential is tending to the decoupled state and so differences become smaller. However, for 35 ppm Cl−, the crack-tip potential for the compact tension specimen exhibited a more modest decrease: 18 mV for the 1 mm crack and 27 mV for the 6 mm crack.
Figure 5 does show that the growth rates for cracks of order 1.5 mm were quite comparable for both compact tension and edge-cracked specimens, albeit based on one test. The remarkable feature of the test with the compact tension specimen with an initial crack size of about 1 mm or so is the dramatic fall-off in growth rate between 1.5 mm and 2.0 mm (failure of the measurement system at this stage limited more extended data). The calculation of crack-tip potential, pH and chloride ion concentration provides broad insight, but we lack the linkage between crack-tip kinetics and these parameters to enable more incisive deductions and predictions. Repeat tests are necessary, but it is likely to be a challenge to explain such sensitivity to crack length over such a limited range should the experimental observations be confirmed.
In conducting the experimental measurements, full immersion was adopted. We have since undertaken preliminary work to model the impact of a thin liquid layer on the potential drop in the crack (Turnbull & Wright, 2017). As expected, the potential drop tended to be greater for condensate thicknesses relevant to service (20 μm and 120 μm). By implication, crack-tip polarisation will be more difficult and requires greater bulk solution conductivity.
A combination of corrosion fatigue and stress corrosion testing of 12Cr steam turbine blade steels combined with crack electrochemistry modelling has demonstrated a significant electrochemical crack size effect on crack growth rates that is inherently strongly dependent on solution conductivity and the potential drop generated between the crack tip and the surface remote from the crack.
What constitutes a short or small crack in conventional engineering or material science parlance may have little relevance to stress corrosion cracking and corrosion fatigue, for which size effects on crack growth rates vary significantly with solution conductivity but can prevail up to crack lengths of 1.5 mm in some cases.
The mechanism of crack growth shows a complex dependence on crack size and solution conductivity.
For corrosion fatigue cracks in aerated and deaerated very low chloride ion solutions of order 300 ppb Cl−, the cracking mechanism for long cracks (6 mm or greater) is deduced to be hydrogen-assisted fatigue. For short cracks (<250 μm in this case) in aerated solution, the mechanism is considered to transfer to anodic dissolution assisted fatigue, but for deaerated solution, a hydrogen-assisted fatigue mechanism prevails. Cracking in all cases was transgranular.
In aerated 35 ppm Cl−, the mechanism of cracking for the long crack is proposed to be hydrogen-assisted fatigue, but for small cracks up to at least 1.5 mm in depth, a superposition of an anodic dissolution controlled stress corrosion mechanism prevailed in one out of three tests and the cracking mode transformed from transgranular for long cracks to intergranular for small cracks.
Stress corrosion cracking for both short, small and long cracks is considered to proceed by an anodic dissolution controlled intergranular cracking mechanism.
This work was conducted as part of a joint venture between the United Kingdom Department for Business, Energy and Industrial Strategy (BEIS), and an industrial group comprising of S. Fenton (Eon UK), D. Gass (Siemens), W. Hahn (EDF Energy), H. Pitts (HSL), S. Osgerby (GE Power), and A. Rowe (RWE npower). Discussion with this group is greatly appreciated, as is the contribution from Liya Guo and Louise Wright from NPL.
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