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Modelling of the evolution of stress corrosion cracks from corrosion pits
Scripta Materialia 54 (2006) 575–578 www.actamat-journals.com
Modelling of the evolution of stress corrosion cracks from corrosion pits A. Turnbull *, L.N. McCartney, S. Zhou Materials Centre, National Physical Laboratory, DEPC, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom Received 25 July 2005; accepted 25 October 2005 Available online 18 November 2005
Abstract A mathematical model has been applied to simulate the evolution of stress corrosion cracks from corrosion pits in the short and long crack domains. The distribution of crack-depths in the short crack domain was well represented and some unique features of pit and crack profiles reproduced. Crown Copyright 2005 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Stress corrosion cracking; Pitting; Modelling
1. Introduction Predicting the evolution of stress corrosion cracks from pits and their subsequent growth has been a major challenge because of the need to address the statistics of pit growth, the transition to a stress corrosion crack, and the subsequent growth in the short and long crack domain. A purely statistical approach has constraints in its predictive capability when addressing the different stages of growth and in accounting for variations in service conditions. However, the strategic significance of such predictions in aerospace and power generation applications has acted as a focal point for research and rapid progress is now being made in modelling, based on deterministic equations with statistically variable input parameters [1–5]. In a previous stage of model development [5], applied to a steam turbine disc steel (3NiCrMoV) in a simulated condensate environment, we demonstrated excellent predictions of the distribution of pit depths with exposure period and of the percentage of pits that transform to cracks, within the constraints of measurement of surfacebreaking cracks. The extension of the model to include the growth of cracks following the pit-to-crack transition
*
Corresponding author. Tel.: +44 20 8943 7115; fax: +44 20 8614 0436. E-mail address: [email protected] (A. Turnbull).
is now described together with unique measurements of the pit and crack-depth distribution. 2. Model details The detailed mathematical elements of the model are described elsewhere [5]. Here, only the most essential features are presented to provide context. 2.1. Initial pit depth distribution and its subsequent evolution The model was developed to incorporate source and sink terms corresponding to pit initiation and deactivation but these features have been neglected for this specific application as we are mainly concerned with the growth of stable pits [5]. The initial distribution of stable pit depths is assumed to be defined by the three-parameter Weibull distribution. The probability that the depth of a corrosion pit lies in the range 0 ! x (i.e. the cumulative probability) is then given by the relation F ðxÞ ¼ 1 exp½1 a1 ðx x0 Þa2 ;
ð1Þ
where a1 and a2 are the Weibull parameters and x0 is the minimum possible depth in the range (25 lm for stable pits in this system [5]). If the pit depth is below x0 then the probability is set to zero. A random number generator is
1359-6462/$ - see front matter Crown Copyright 2005 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.scriptamat.2005.10.053
A. Turnbull et al. / Scripta Materialia 54 (2006) 575–578
adopted when calculating the initial set of corrosion pit depths to reflect the statistical variability of the data, recognising that every exposure test would generate a different distribution of pit depths. In practice, it was shown [5] that the evolution of pit depths is dominated by the growth law with little sensitivity to the initial distribution except at short times. For a given surface area, P(x, t)dx is the number of pits at time t having depth in the range x ! x + dx. It can be demonstrated that the evolution of the pit depth distribution function P(x, t) from an initial stable population is governed by the partial differential equation oP ðx; tÞ o ¼ ½gðxÞP ðx; tÞ þ Sðx; tÞ; ot ox
da/dt = Const
1E-11
(deep crack data)
1E-12 da/dt = Cσ6a3
1E-13 1E-14
(based on pit-crack trans.) 100 µm
ð2Þ
ð3Þ
and, from (3), the growth rate has the form: dx ¼ gðxÞ ¼ ba1=b xð11=bÞ . dt
1E-10
0.01
where g(x) is the growth rate of a pit having depth x and S(x, t) is the number of pits of depth in the range x ! x + dx which are nucleated in the given area of the exposed surface during the time interval dt. The latter term is included for generality but since we are considering a stable pit depth distribution, for which pits do not deactivate and no new pits grow into this depth range, it may be neglected for this application. It is assumed that the depth can be described by x ¼ atb
1E-9 Crack growth rate / m s-1
576
ð4Þ
It is readily demonstrated that the pit growth rate must be statistically distributed [5]. In conducting the analysis it was assumed that b is a constant that has to be derived and that a is also unknown but distributed normally. In practice, it is only the distribution of pit growth rates that matters rather than the form of the individual parameters so this is not a constraining assumption. The numerical approach involves selecting each pit depth at random and allocating a possible value of a selected at random from a normal distribution (negative values are rejected as being physically not meaningful). 2.2. Pit-to-crack transition and the early stages of crack growth Previously, we adopted the criteria of Kondo [1] and assumed that the transition occurred when the pit depth was above the critical pit depth (representing a threshold mechanical driving force) AND the crack growth rate was greater than the pit growth rate. However, we now make the additional assumption that the pit growth rate must be greater than a certain minimum value. Statistically, extremely low pit growth rates might be predicted and, as such, a pit-to-crack transition is inherently assured. Physically, such slow pit growth rates would be tantamount to considering the pit as effectively deactivated. This was not accounted for in the previous model, and has only a marginal effect, but for completeness was included herein.
1 cm
a1/2 / m1/2
0.1
Fig. 1. Calculated mean crack growth rates at the pit-to-crack transition and average long crack growth kinetics. Arrows highlight the requirement for the transition to long crack growth kinetics at some critical crackdepth.
In the previous model, for which only the pit-to-crack transition was explored [5], the crack growth law assumed was specified by dx ¼ Crp xq ; dt
ð5Þ
where the flaw depth is described by x and the parameter C is considered to be statistically distributed, selected at random from a normal distribution. However, such a growth law would lead to the growth rate of propagating cracks continuing to accelerate with increasing crack depth in contrast to experimental observation that the growth rate for deep cracks tends to be constant, independent of the stress intensity factor, for a specific environmental condition. Thus, the key advance in this version of the model is to include a feature that enables the crack growth rate as defined by Eq. (5) to transform to that for a deep crack beyond a certain depth (Fig. 1). The absence of any information on short crack growth in this system (and indeed for stress corrosion cracking in general) has necessitated a rather blunt approach to the transition based on the adoption of a critical crack-depth for the transition in growth rate. This inevitably results in a step-wise decrease or increase depending on the distribution of crack growth rates. Accelerated crack growth rate in the short crack regime is not an unusual phenomenon, being commonly observed in fatigue crack growth. Similarly, the concept that cracks will behave like deep cracks above a certain crack-depth is recognised. The evaluation of this upgraded model will now be described using new experimental data for the crack-depth distribution. 3. Results and discussion The model is applied to stress corrosion tests conducted on a 3NiCrMoV disc steel using pit and crack-depth measurements from self-loaded specimens exposed to aerated
A. Turnbull et al. / Scripta Materialia 54 (2006) 575–578
1.5 ppm chloride solution after 9187 h. From the fit to the data (pitting and surface-breaking cracks) at different exposure times, values of the relevant parameters in Eq. (5) had been derived previously [5]. The predicted crack-depth dependence of the mean crack growth rate is shown in Fig. 1. The mean value of C was 2.6 · 1018 MPa m2 s1 and the standard deviation 3.8 · 1018 MPa m2 s1 at the test temperature of 90 C. The deep crack growth rate was based on measurements of the same steel in aerated 1.5 ppm Cl using fracture mechanics specimens [6,7]. The repeatability of laboratory measurements suggests that there is no significant statistical variability in long crack growth rates. The data used to fit and test the model were based on measurements of the pit and crack-depth distribution using the layer removal technique [8]. Such detailed information on stress corrosion crack-depth distribution in the short crack domain is wholly unique and has not been reported. Unexpected features of the pit and crack profiles were observed, illustrated schematically in Fig. 2. Quantitatively, 43% of cracks present extended beyond the base of the pit and also broke the surface in the expected manner. However, 50% broke the surface but the pit base was deeper than the crack, and 7% extended beyond the pit base but did not break the surface. There were one or two cracks that appeared at the side of the pit but did not extend to either the base of the pit or the surface. The model has to explain the observed behaviour of Fig. 2 and also predict the crack-depth distribution. In the latter case, there is an issue in defining what we mean
P
C
577
by the crack-depth. We defined the crack-depth in terms of the magnitude of the extension beyond the base of the pit, at its maximum depth, plus the pit depth itself at that location. Cracks for which the associated pits were of greater depth were not considered. The data for this exposure condition and an exposure period of 9187 h are shown in Fig. 3. In applying the model to this data, the only adjustable parameter is the value of the critical crack-depth for the transition to the deep crack growth rate. The deep crack growth rate was fixed and all other data were as derived in fitting previously to the pitting data and in deriving the expression for the crack growth rate in the form of Eq. (5). The model captures well the essential features of the distribution of crack-depths (Fig. 3) using a value of 600 lm for the critical depth for the transition in growth rate. The range is well predicted, although the number of cracks at a given crack-depth was somewhat greater. Repeat runs at transition depths of 550 lm or 650 lm did not give satisfactory fits to the data. The possibility of a change in the fracture mode at this magnitude of crackdepth is being explored since it is perceived that short cracks in these turbine disc steels tend to be predominantly transgranular and deep cracks intergranular [9]. An interesting feature from the model was the prediction of pits extending beyond the crack, as observed experimentally. In this model calculation, 12% of all cracks were of this characteristic. This was significantly smaller than measured (50%) and explains the higher density of cracks predicted in Fig. 3. The prediction of such pit/crack configurations is unique and consistent with a transition in growth rate, although the step-wise nature assumed is very crude. Initially, the crack growth rate exceeds the pit growth rate, leading to the pit-to-crack transition. Bear in mind the statistical nature of the growth rate here also. However, as the crack extends, the transition to the slower deep crack growth kinetics ensues. Although the pit growth
7 C
Expt Model
6 Number of cracks
P
5 4 3 2 1
P
0 0 C
Fig. 2. Schematic illustration of pit (P) and crack (C) shapes showing pits with cracks extending beyond pit base and breaking surface, pits extending beyond the crack, and cracks just emanating from pit base but not extending to surface.
200
400
600
800
Total Depth / µm Fig. 3. Comparison of model prediction and experimental measurement of crack-depth distribution for turbine disc steel in 1.5 ppm Cl at 90 C after 9187 h exposure. The total depth refers to the distance from the surface and includes the pit depth and the extension of the crack beyond the pit base. Cracks with pit depths extending beyond the crack base are not included.
578
A. Turnbull et al. / Scripta Materialia 54 (2006) 575–578
Number of cracks in size range
30 30 years
5 years
20
of extreme crack-depths and use this distribution as one input to a structural integrity assessment. Inclusion of transient behaviour is also feasible. 4. Conclusions
10
long crack growth only9500µm
long crack growth only 1580µm
0 0
2000
4000
6000
8000
10000 12000
Total depth /µm Fig. 4. Model-based projection of the distribution of crack-depths after long-term exposure of disc steel to aerated chloride solution. Estimated depths based on the long crack growth data are shown.
rate also falls off with pit depth, the rate is sufficient in some cases to exceed the deep crack growth rate. Thus, the pit catches up with the crack and then extends beyond it. This rationale does not preclude the possibility that cracks may emanate from the side of the pits directly and such a possibility may explain the difference between model predictions and experiment. The ability to predict the crack-depth distribution so well and also, uniquely, pit depths extending beyond the previously initiated crack, is quite remarkable and very encouraging. Nevertheless, in view of the sparseness of experimental data, extension to other exposure periods is important to enhance confidence. There are limitations. The adoption of a sharp transition in growth rates is artificial; a more gradual transition is to be expected. Furthermore, there is no independent measurement of crack growth rates in the short crack regime. The latter presents a challenge in measurement that we are addressing. The aim of this type of modelling is to improve the basis of prediction in service. More research is being undertaken to understand the role of service transients but an illustration of the potential for long-term predictions is shown in Fig. 4. Here, 5-year and 30-year model-based projections of the crack-depth distribution are compared with calculations assuming long crack growth only with the crack assumed initiated at time zero. It is evident that the estimates based on the long crack growth data underestimate the depth of the deepest cracks, especially at the short exposure period, as might be expected. In applying our model we would envisage repeated application to generate the distribution
• The model for pitting and the transition from pits to stress corrosion cracks has now been successfully extended to include the evolution of the crack-depth distribution yielding predictions reasonably consistent with available experimental data. • Unique experimental measurements indicate that almost 50% of cracks associated with pits had pit depths that extended beyond the deepest point of the crack. • The model does predict such profiles but to a reduced extent compared with measurement.
Acknowledgements This work was conducted as part of the Performance of Materials programme, a joint venture between the United Kingdom Department of Trade and Industry and an Industrial Group comprising Douglas Gass (Siemens), Sarah Harris (BNFL Magnox), Stuart Holdsworth (Alstom), Paul McIntyre (IOMMM), Paul Mulvihill (Powergen), Terry Parsons (BNFL Magnox), Neville Shaw (Innogy) and Mike Tookey (British Energy). References [1] Kondo Y. Corrosion 1989;45:7. [2] Wei RP. Material aging and reliability of engineered systems, in: Proceedings of conference on Environmentally Assisted Cracking: Predictive methods for risk assessment and evaluation of material, equipment and structures, editor R.D. Kane, ASTM STP1401, 2000, pp. 3–19. [3] Engelhardt G, Macdonald DD, Zhang Y, Dooley B. Power Plant Chem 2004;6:647. [4] Engelhardt G, Macdonald DD. Corros Sci 2004;46:2755. [5] Turnbull A., McCartney LN, Zhou S. A deterministic model of pitting corrosion and the pit-to-crack transition, Corros Sci, in press, 2005. [6] Zhou S, Turnbull A. Environment assisted cracking of steam turbine disc and blade steels—Description of test procedure and preliminary results, NPL Report MAT(C) A41, 2001. [7] Zhou S, Turnbull A. Effect of Stress Transients on the Crack Propagation Rate in Steam Turbine Disc Steel, Corrosion, accepted for publication. [8] Turnbull A., Zhou S, Orkney L, McCormick N. Visualisation of Stress Corrosion Cracks Emerging from Pits, Corrosion, submitted for publication. [9] Turnbull A, Zhou A. Corros Eng Sci Technol 2003;38:177.
Modelling of the evolution of stress corrosion cracks from corrosion pits A. Turnbull *, L.N. McCartney, S. Zhou Materials Centre, National Physical Laboratory, DEPC, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom Received 25 July 2005; accepted 25 October 2005 Available online 18 November 2005
Abstract A mathematical model has been applied to simulate the evolution of stress corrosion cracks from corrosion pits in the short and long crack domains. The distribution of crack-depths in the short crack domain was well represented and some unique features of pit and crack profiles reproduced. Crown Copyright 2005 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Stress corrosion cracking; Pitting; Modelling
1. Introduction Predicting the evolution of stress corrosion cracks from pits and their subsequent growth has been a major challenge because of the need to address the statistics of pit growth, the transition to a stress corrosion crack, and the subsequent growth in the short and long crack domain. A purely statistical approach has constraints in its predictive capability when addressing the different stages of growth and in accounting for variations in service conditions. However, the strategic significance of such predictions in aerospace and power generation applications has acted as a focal point for research and rapid progress is now being made in modelling, based on deterministic equations with statistically variable input parameters [1–5]. In a previous stage of model development [5], applied to a steam turbine disc steel (3NiCrMoV) in a simulated condensate environment, we demonstrated excellent predictions of the distribution of pit depths with exposure period and of the percentage of pits that transform to cracks, within the constraints of measurement of surfacebreaking cracks. The extension of the model to include the growth of cracks following the pit-to-crack transition
*
Corresponding author. Tel.: +44 20 8943 7115; fax: +44 20 8614 0436. E-mail address: [email protected] (A. Turnbull).
is now described together with unique measurements of the pit and crack-depth distribution. 2. Model details The detailed mathematical elements of the model are described elsewhere [5]. Here, only the most essential features are presented to provide context. 2.1. Initial pit depth distribution and its subsequent evolution The model was developed to incorporate source and sink terms corresponding to pit initiation and deactivation but these features have been neglected for this specific application as we are mainly concerned with the growth of stable pits [5]. The initial distribution of stable pit depths is assumed to be defined by the three-parameter Weibull distribution. The probability that the depth of a corrosion pit lies in the range 0 ! x (i.e. the cumulative probability) is then given by the relation F ðxÞ ¼ 1 exp½1 a1 ðx x0 Þa2 ;
ð1Þ
where a1 and a2 are the Weibull parameters and x0 is the minimum possible depth in the range (25 lm for stable pits in this system [5]). If the pit depth is below x0 then the probability is set to zero. A random number generator is
1359-6462/$ - see front matter Crown Copyright 2005 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.scriptamat.2005.10.053
A. Turnbull et al. / Scripta Materialia 54 (2006) 575–578
adopted when calculating the initial set of corrosion pit depths to reflect the statistical variability of the data, recognising that every exposure test would generate a different distribution of pit depths. In practice, it was shown [5] that the evolution of pit depths is dominated by the growth law with little sensitivity to the initial distribution except at short times. For a given surface area, P(x, t)dx is the number of pits at time t having depth in the range x ! x + dx. It can be demonstrated that the evolution of the pit depth distribution function P(x, t) from an initial stable population is governed by the partial differential equation oP ðx; tÞ o ¼ ½gðxÞP ðx; tÞ þ Sðx; tÞ; ot ox
da/dt = Const
1E-11
(deep crack data)
1E-12 da/dt = Cσ6a3
1E-13 1E-14
(based on pit-crack trans.) 100 µm
ð2Þ
ð3Þ
and, from (3), the growth rate has the form: dx ¼ gðxÞ ¼ ba1=b xð11=bÞ . dt
1E-10
0.01
where g(x) is the growth rate of a pit having depth x and S(x, t) is the number of pits of depth in the range x ! x + dx which are nucleated in the given area of the exposed surface during the time interval dt. The latter term is included for generality but since we are considering a stable pit depth distribution, for which pits do not deactivate and no new pits grow into this depth range, it may be neglected for this application. It is assumed that the depth can be described by x ¼ atb
1E-9 Crack growth rate / m s-1
576
ð4Þ
It is readily demonstrated that the pit growth rate must be statistically distributed [5]. In conducting the analysis it was assumed that b is a constant that has to be derived and that a is also unknown but distributed normally. In practice, it is only the distribution of pit growth rates that matters rather than the form of the individual parameters so this is not a constraining assumption. The numerical approach involves selecting each pit depth at random and allocating a possible value of a selected at random from a normal distribution (negative values are rejected as being physically not meaningful). 2.2. Pit-to-crack transition and the early stages of crack growth Previously, we adopted the criteria of Kondo [1] and assumed that the transition occurred when the pit depth was above the critical pit depth (representing a threshold mechanical driving force) AND the crack growth rate was greater than the pit growth rate. However, we now make the additional assumption that the pit growth rate must be greater than a certain minimum value. Statistically, extremely low pit growth rates might be predicted and, as such, a pit-to-crack transition is inherently assured. Physically, such slow pit growth rates would be tantamount to considering the pit as effectively deactivated. This was not accounted for in the previous model, and has only a marginal effect, but for completeness was included herein.
1 cm
a1/2 / m1/2
0.1
Fig. 1. Calculated mean crack growth rates at the pit-to-crack transition and average long crack growth kinetics. Arrows highlight the requirement for the transition to long crack growth kinetics at some critical crackdepth.
In the previous model, for which only the pit-to-crack transition was explored [5], the crack growth law assumed was specified by dx ¼ Crp xq ; dt
ð5Þ
where the flaw depth is described by x and the parameter C is considered to be statistically distributed, selected at random from a normal distribution. However, such a growth law would lead to the growth rate of propagating cracks continuing to accelerate with increasing crack depth in contrast to experimental observation that the growth rate for deep cracks tends to be constant, independent of the stress intensity factor, for a specific environmental condition. Thus, the key advance in this version of the model is to include a feature that enables the crack growth rate as defined by Eq. (5) to transform to that for a deep crack beyond a certain depth (Fig. 1). The absence of any information on short crack growth in this system (and indeed for stress corrosion cracking in general) has necessitated a rather blunt approach to the transition based on the adoption of a critical crack-depth for the transition in growth rate. This inevitably results in a step-wise decrease or increase depending on the distribution of crack growth rates. Accelerated crack growth rate in the short crack regime is not an unusual phenomenon, being commonly observed in fatigue crack growth. Similarly, the concept that cracks will behave like deep cracks above a certain crack-depth is recognised. The evaluation of this upgraded model will now be described using new experimental data for the crack-depth distribution. 3. Results and discussion The model is applied to stress corrosion tests conducted on a 3NiCrMoV disc steel using pit and crack-depth measurements from self-loaded specimens exposed to aerated
A. Turnbull et al. / Scripta Materialia 54 (2006) 575–578
1.5 ppm chloride solution after 9187 h. From the fit to the data (pitting and surface-breaking cracks) at different exposure times, values of the relevant parameters in Eq. (5) had been derived previously [5]. The predicted crack-depth dependence of the mean crack growth rate is shown in Fig. 1. The mean value of C was 2.6 · 1018 MPa m2 s1 and the standard deviation 3.8 · 1018 MPa m2 s1 at the test temperature of 90 C. The deep crack growth rate was based on measurements of the same steel in aerated 1.5 ppm Cl using fracture mechanics specimens [6,7]. The repeatability of laboratory measurements suggests that there is no significant statistical variability in long crack growth rates. The data used to fit and test the model were based on measurements of the pit and crack-depth distribution using the layer removal technique [8]. Such detailed information on stress corrosion crack-depth distribution in the short crack domain is wholly unique and has not been reported. Unexpected features of the pit and crack profiles were observed, illustrated schematically in Fig. 2. Quantitatively, 43% of cracks present extended beyond the base of the pit and also broke the surface in the expected manner. However, 50% broke the surface but the pit base was deeper than the crack, and 7% extended beyond the pit base but did not break the surface. There were one or two cracks that appeared at the side of the pit but did not extend to either the base of the pit or the surface. The model has to explain the observed behaviour of Fig. 2 and also predict the crack-depth distribution. In the latter case, there is an issue in defining what we mean
P
C
577
by the crack-depth. We defined the crack-depth in terms of the magnitude of the extension beyond the base of the pit, at its maximum depth, plus the pit depth itself at that location. Cracks for which the associated pits were of greater depth were not considered. The data for this exposure condition and an exposure period of 9187 h are shown in Fig. 3. In applying the model to this data, the only adjustable parameter is the value of the critical crack-depth for the transition to the deep crack growth rate. The deep crack growth rate was fixed and all other data were as derived in fitting previously to the pitting data and in deriving the expression for the crack growth rate in the form of Eq. (5). The model captures well the essential features of the distribution of crack-depths (Fig. 3) using a value of 600 lm for the critical depth for the transition in growth rate. The range is well predicted, although the number of cracks at a given crack-depth was somewhat greater. Repeat runs at transition depths of 550 lm or 650 lm did not give satisfactory fits to the data. The possibility of a change in the fracture mode at this magnitude of crackdepth is being explored since it is perceived that short cracks in these turbine disc steels tend to be predominantly transgranular and deep cracks intergranular [9]. An interesting feature from the model was the prediction of pits extending beyond the crack, as observed experimentally. In this model calculation, 12% of all cracks were of this characteristic. This was significantly smaller than measured (50%) and explains the higher density of cracks predicted in Fig. 3. The prediction of such pit/crack configurations is unique and consistent with a transition in growth rate, although the step-wise nature assumed is very crude. Initially, the crack growth rate exceeds the pit growth rate, leading to the pit-to-crack transition. Bear in mind the statistical nature of the growth rate here also. However, as the crack extends, the transition to the slower deep crack growth kinetics ensues. Although the pit growth
7 C
Expt Model
6 Number of cracks
P
5 4 3 2 1
P
0 0 C
Fig. 2. Schematic illustration of pit (P) and crack (C) shapes showing pits with cracks extending beyond pit base and breaking surface, pits extending beyond the crack, and cracks just emanating from pit base but not extending to surface.
200
400
600
800
Total Depth / µm Fig. 3. Comparison of model prediction and experimental measurement of crack-depth distribution for turbine disc steel in 1.5 ppm Cl at 90 C after 9187 h exposure. The total depth refers to the distance from the surface and includes the pit depth and the extension of the crack beyond the pit base. Cracks with pit depths extending beyond the crack base are not included.
578
A. Turnbull et al. / Scripta Materialia 54 (2006) 575–578
Number of cracks in size range
30 30 years
5 years
20
of extreme crack-depths and use this distribution as one input to a structural integrity assessment. Inclusion of transient behaviour is also feasible. 4. Conclusions
10
long crack growth only9500µm
long crack growth only 1580µm
0 0
2000
4000
6000
8000
10000 12000
Total depth /µm Fig. 4. Model-based projection of the distribution of crack-depths after long-term exposure of disc steel to aerated chloride solution. Estimated depths based on the long crack growth data are shown.
rate also falls off with pit depth, the rate is sufficient in some cases to exceed the deep crack growth rate. Thus, the pit catches up with the crack and then extends beyond it. This rationale does not preclude the possibility that cracks may emanate from the side of the pits directly and such a possibility may explain the difference between model predictions and experiment. The ability to predict the crack-depth distribution so well and also, uniquely, pit depths extending beyond the previously initiated crack, is quite remarkable and very encouraging. Nevertheless, in view of the sparseness of experimental data, extension to other exposure periods is important to enhance confidence. There are limitations. The adoption of a sharp transition in growth rates is artificial; a more gradual transition is to be expected. Furthermore, there is no independent measurement of crack growth rates in the short crack regime. The latter presents a challenge in measurement that we are addressing. The aim of this type of modelling is to improve the basis of prediction in service. More research is being undertaken to understand the role of service transients but an illustration of the potential for long-term predictions is shown in Fig. 4. Here, 5-year and 30-year model-based projections of the crack-depth distribution are compared with calculations assuming long crack growth only with the crack assumed initiated at time zero. It is evident that the estimates based on the long crack growth data underestimate the depth of the deepest cracks, especially at the short exposure period, as might be expected. In applying our model we would envisage repeated application to generate the distribution
• The model for pitting and the transition from pits to stress corrosion cracks has now been successfully extended to include the evolution of the crack-depth distribution yielding predictions reasonably consistent with available experimental data. • Unique experimental measurements indicate that almost 50% of cracks associated with pits had pit depths that extended beyond the deepest point of the crack. • The model does predict such profiles but to a reduced extent compared with measurement.
Acknowledgements This work was conducted as part of the Performance of Materials programme, a joint venture between the United Kingdom Department of Trade and Industry and an Industrial Group comprising Douglas Gass (Siemens), Sarah Harris (BNFL Magnox), Stuart Holdsworth (Alstom), Paul McIntyre (IOMMM), Paul Mulvihill (Powergen), Terry Parsons (BNFL Magnox), Neville Shaw (Innogy) and Mike Tookey (British Energy). References [1] Kondo Y. Corrosion 1989;45:7. [2] Wei RP. Material aging and reliability of engineered systems, in: Proceedings of conference on Environmentally Assisted Cracking: Predictive methods for risk assessment and evaluation of material, equipment and structures, editor R.D. Kane, ASTM STP1401, 2000, pp. 3–19. [3] Engelhardt G, Macdonald DD, Zhang Y, Dooley B. Power Plant Chem 2004;6:647. [4] Engelhardt G, Macdonald DD. Corros Sci 2004;46:2755. [5] Turnbull A., McCartney LN, Zhou S. A deterministic model of pitting corrosion and the pit-to-crack transition, Corros Sci, in press, 2005. [6] Zhou S, Turnbull A. Environment assisted cracking of steam turbine disc and blade steels—Description of test procedure and preliminary results, NPL Report MAT(C) A41, 2001. [7] Zhou S, Turnbull A. Effect of Stress Transients on the Crack Propagation Rate in Steam Turbine Disc Steel, Corrosion, accepted for publication. [8] Turnbull A., Zhou S, Orkney L, McCormick N. Visualisation of Stress Corrosion Cracks Emerging from Pits, Corrosion, submitted for publication. [9] Turnbull A, Zhou A. Corros Eng Sci Technol 2003;38:177.